Keywords: Machine Learning and Data Mining
Abstract: In this talk, I will explore the use of recent techniques from probabilistic non-parametric machine learning to system identification and control. In this framework, the simultaneous tasks of inferring dynamics and designing a controller is thought of as a statistical inference problem. Conventionally, stochastic models (such as Gaussians) have been used ubiquitously to characterise noise and disturbances; here I will show how the Gaussian (slightly extended to a Gaussian process), can also naturally be used to model the (partially unknown) system dynamics.

Thus, the inference problem is solved with Gaussian processes, using no task specific prior knowledge. Traditional wisdom may suggest that learning without strong prior information will be impractically slow, but I show that provided that uncertainties in the learned dynamics are carefully characterised, learning can be extremely rapid, and result in highly practical tools. The methods are demonstrated on a variety of control problems.

Keywords: Basis Functions, Time Series, Mechanical and Aerospace
Abstract: Functional Series Time-dependent Autoregressive Moving Average (FS-TARMA) models are effective for representing non-stationary random signals arising in a wide variety of applications. Yet, their identification is challenging as, in addition to coefficient of projection estimation, subspace basis function selection is also required. In this study these difficulties are alleviated by postulating adaptive FS-TARMA models, that is models with adaptable basis functions, and a method for their effective identification. This is accomplished via proper basis function parametrizations and a Separable Nonlinear Least Squares (SNLS) type procedure which leads to a reduced dimensionality, constrained, non-quadratic optimization problem tackled via Particle Swarm Optimization (PSO) and gradient-type refinement. The model orders and subspace dimensionalities are also estimated based on PSO optimization and suitable criteria. The method's effectiveness is confirmed via a Monte Carlo study and comparisons with current schemes.

Keywords: Subspace Methods, Mechanical and Aerospace, Vibration and Modal Analysis
Abstract: In this paper, an extension of the output-only subspace identification, to the class of linear periodically time-varying (LPTV) systems, is proposed. The goal is to identify a useful information about the system's stability using the Floquet theory which gives a necessary and sufficient condition for stability analysis. This information is retrieved from a matrix called the monodromy matrix, which is extracted by some simultaneous singular value decompositions (SVD) and from a resolution of a least squares criterion. The method is, finally, illustrated by a simulation of a model of a helicopter with a hinged-blades rotor.

Keywords: Continuous Time System Estimation, Basis Functions, Mechanical and Aerospace
Abstract: This paper introduces a parameter identification method for linear time-varying systems that is based on the derivative formulation of the Chebyshev polynomial basis. A dynamic system matrix representation is first developed for N-DOF mechanical systems having multiple time-varying parameters. The method is then applied to a numerical simulation of a rotational 1-DOF mechanical system having time-varying stiffness, constant damping, and constant inertia. Results show that the identification quality is significantly increased when the least-square identification is performed only with the center portion of the time basis of the Chebyshev basis used.

Keywords: Nonlinear System Identification, Bayesian Methods, Biological Systems
Abstract: Nonlinear Bayesian filtering offers various online tools for system identification of parametric ordinary differential equation models. Since parameters may change with time, it is a relevant question to assess how well time-varying parameters can be estimated. For this purpose we tested two filtering methods, Extended Kalman Filter and Particle Filter for joint state and time-varying parameter estimation on a dynamic model of HIV-1 virus immune response. After evaluating the methods on simulated time-series we applied them to clinical datasets. Estimated time-varying parameters on clinical data are consistent with previously reported results with offline algorithms.

Keywords: Nonlinear System Identification, Grey Box Modelling, Machine Learning and Data Mining
Abstract: This paper develops a new approach based on Least Squares Support Vector Machines (LS-SVMs) for parameter estimation of time invariant as well as time varying dynamical SISO systems. Closed-form approximate models for the state and its derivative are first derived from the observed data by means of LS-SVMs. The time-derivative information is then substituted into the system of ODEs, converting the parameter estimation problem into an algebraic optimization problem. In the case of time invariant systems one can use least-squares to solve the obtained system of algebraic equations. The estimation of time-varying coefficients in SISO models, is obtained by assuming an LS-SVM model for it.

Keywords: Biological Systems, Nonparametric Methods
Abstract: There are many challenges to designing a prosthetic limb capable of restoring natural movements. One of these is that it should replicate the complex, time varying behavior of the original limb so as to restore natural interactions with the environment. Unfortunately, there are many experimental and computational challenges associated with obtaining accurate estimates of limb impedance during movement. Here we present a time-varying system identification algorithm suitable for this purpose, and demonstrate how it can be used to estimate the impedance of the human knee during time-varying conditions relevant to locomotion.

Keywords: Input and Excitation Design, Biological Systems, Identification for Control
Abstract: We examine some of the challenges associated with generating input signals for identifying dynamics in pain treatment interventions while imposing "patient-friendly" constraints on the design. Standard clinical trials, while providing some useful information, are not the most suitable vehicle for understanding the dynamic response of dosage changes to participant response. Meanwhile, much of the work in classical input design, even that which incorporates "plant-friendly" considerations, may not result in clinically acceptable trials for human participants. In this paper, we describe some of the issues involved and suggest various approaches (leading ultimately to optimization-based formulations) to obtain input signals with desired spectral properties under time-domain constraints of importance to clinical practice. Numerical examples are shown to illustrate the proposed method with a hypothetical clinical trial of the drug gabapentin for the treatment of neuropathic pain.

Keywords: Input and Excitation Design, Nonlinear System Identification, Continuous Time System Estimation
Abstract: An approach is proposed to joint activation of stationary sensor nodes and design of mobile sensor trajectories in a hybrid sensor network collecting measurements for parameter estimation of a process described by a partial differential equation. The ultimate objective is maximization of the log-determinant of the information matrix associated with the estimated parameters. The search for the optimal solution is performed using the branch-and-bound method in which a block coordinate ascent method is employed to produce an upper bound to the maximum objective function. It alternates between solving a relaxed combinatorial problem for the selection of active stationary nodes and a relaxed optimal control problem for the design of sensor trajectories. The former is achieved using a simplicial decomposition algorithm in which the restricted master problem is solved using a multiplicative algorithm for optimal design. In turn, the latter is solved by another algorithm for optimal design, namely the Wynn-Fedorov algorithm, which is capable of finding an optimal element in the convex hull of the set of attainable information matrices and can be easily implemented by using a standard optimal control solver as its component.

Keywords: Nonlinear System Identification, Input and Excitation Design, Frequency Domain Identification
Abstract: This paper compares the performance of three different types of periodic binary sequences in the identification of the Best Linear Approximation of a nonlinear system. The signal types considered are discrete interval random binary sequences (DIRBS), maximum length binary sequences (MLBS) and inverse-repeat binary sequences (IRBS). It is found that MLBS’s offer advantages when experiment time limitation prohibits a large amount of averaging. IRBS’s have the advantage that even order nonlinear contributions do not affect the quality of the estimate, but the disadvantage of either a longer experiment time or a lower frequency resolution.

Keywords: Input and Excitation Design, Fault Detection and Diagnosis, Frequency Domain Identification
Abstract: Renewable energy, such as solar and wind, is usually connected to a power grid through grid-parallel inverters. The impedance mismatch between the grid and the interfacing circuit often generates harmonic resonances which leads to reduced power quality. Recent studies have shown that the problem can be approached through impedance models that may be obtained by broadband excitation and cross-correlation technique. However, the inverters are affected by the sinusoidal (AC) grid voltage, which necessitates modifications to the state-of-art techniques designed for DC systems. This paper considers the modifications and proposes methods for obtaining impedance models for AC-connected systems.

Keywords: Input and Excitation Design, Identification for Control
Abstract: Optimal experiment or input design is the scientific exercise of designing informative excitation signals for the identification of a real-life dynamic system. In the least costly input design framework, the input is designed such that the identification cost is minimized while meeting desired specifications on the quality of the identified model. Identification of real-life processes require that the identification be “plant-friendly”. These are typically imposed as constraints on experiment time, input and output amplitudes or input move sizes. This work focusses on an LMI based plant friendly input design in the least costly framework.

Keywords: Fault Detection and Diagnosis, Nonlinear System Identification, Closed Loop Identification
Abstract: This paper uses prediction error identification to distinguish control-relevant system changes in closed-loop operation from variations in disturbance characteristics. The approach consists of a hypothesis test to verify whether an identified model of the true system lies in a set containing all models that exhibit adequate closed-loop performance. To increase the detection probability, i.e. the probability of choosing the correct hypothesis, experiment design is performed to devise an excitation signal for closed-loop identification of the system dynamics. For a given identification cost, this allows us to maximize the probability that an identified model of the system lies in the performance-related region of interest in accordance with the hypothesis test and, therefore, decrease the probability of opting for an erroneous hypothesis.

Keywords: Errors in Variables Identification, Identifiability
Abstract: When identifying a dynamic system the model order has to be determined unless it is a priori known. For an errors-in-variables situation where both input and output measurements are noise corrupted, this is a nontrivial task, seldom treated in the literature. Some different approaches for model order determination are introduced and evaluated by theoretical analysis as well as application to simulated data and to a real-life case study.

Keywords: Errors in Variables Identification
Abstract: This paper deals with the identification of errors–in–variables models where the additive input and output noises are mutually correlated white processes. The proposed solution is based on the extension of the dynamic Frisch scheme introduced in (Beghelli et al., 1990). First, a geometric characterization of the whole set of admissible solutions in the noise space is described. Then, a criterion that allows to select the solution of the identification problem inside the locus is proposed. This criterion relies on the properties of a set of high–order Yule–Walker equations. The effectiveness of this identification approach is tested by means of Monte Carlo simulations.

Keywords: Errors in Variables Identification, Maximum Likelihood Methods, Frequency Domain Identification
Abstract: In this paper we develop a novel identification algorithm for Errors-in-Variables systems (represented in transfer function form) using incomplete data. We propose a Maximum Likelihood formulation in the frequency domain that considers a restricted of a frequency range from the available measurements.

Keywords: Errors in Variables Identification, Frequency Domain Identification
Abstract: Using nonparametric noise models the complexity of the errors-in-variables problem is reduced to that of a generalised output error problem. Via experiments with periodic excitation signals one can easily obtain nonparametric estimates of the input-output noise models in a preprocessing step. The following assumptions are hereby made: (i) the system operates in steady state, (ii) at least P=7 signal periods are available, and (iii) consecutive signal periods are independently distributed. Due to the noise colouring, assumption (iii) is an approximation. In addition assumptions (i) and (ii) reduce the frequency resolution of the experiment. In this paper we present a method that handles these three restrictions: 2 periods of the transient response to a periodic excitation are sufficient, and the correlation among consecutive signal periods is suppressed.

Keywords: Errors in Variables Identification
Abstract: The multiple input multiple output errors-in-variables problem is considered and it is shown how the problem can be solved by means of covariance matching. A right matrix fraction description is used for the transfer function and some covariance relations are derived. Based on these covariance relations and a set of estimated covariances from the data, an estimator in the form of a separable least squares problem is proposed. A user choice of which covariances to consider must be made. Different types of parameterizations can be considered for the estimation algorithm. Some properties of the method are illustrated in numerical examples.

Keywords: Filtering and Smoothing
Abstract: In this paper an approach for reconstructing an unknown input in the case when input and output signals are both subject to measurement uncertainties, i.e. errors-in-variables framework, is presented. The algorithm is applicable to Hammerstein-Wiener systems, i.e. systems composed from a dynamic linear system followed and preceded by a memoryless nonlinearity. It is based on a parity equations concept and forms an extension of the idea developed previously by the authors for linear systems. The only requirement is that the function used to describe the component static output nonlinearity must be strictly monotonic. The order of the parity space can be treated as a tuning parameter allowing for a trade-off between the smoothness of the reconstructed unknown input and a phase lag to be obtained. An analytical solution of the overall problem is obtained by using a Lagrange multiplier method.

Keywords: Errors in Variables Identification, Continuous Time System Estimation
Abstract: A covariance matching method for continuous-time errors-in-variables system identification from discrete-time data is analyzed. The asymptotic normalized covariance matrix, valid for a large number of data and a small sampling interval, is evaluated. This involves the evaluation of a covariance matrix of estimated covariance elements and estimated derivatives of such elements, and large parts of the paper are devoted to this task.

Keywords: Nonlinear System Identification, Closed Loop Identification, Mechanical and Aerospace
Abstract: Off-line robot dynamic identification methods are based on the use of the Inverse Dynamic Identification Model (IDIM), which calculates the joint forces/torques that are linear in relation to the dynamic parameters, and on the use of linear least squares technique to calculate the parameters (IDIM-LS technique). The joint forces/torques are calculated as the product of the known control signal (the current reference) by the joint drive gains. Then it is essential to get accurate values of joint drive gains to get accurate identification of inertial parameters. In the previous works, it was proposed to identify each gain separately. This does not allow taking into account the dynamic coupling between the robot axes. In this paper the global joint drive gains parameters of all joints are calculated simultaneously. The method is based on the weighted total least squares solution of an over-determined linear system obtained with the inverse dynamic model calculated with available current reference and position sampled data while the robot is tracking one reference trajectory without load on the robot and one trajectory with a known payload fixed on the robot. The method is experimentally validated on an industrial 6 joint Stäubli TX-40 robot.

Keywords: Nonlinear System Identification, Mechanical and Aerospace, Hybrid and Distributed System Identification
Abstract: Once dynamic process models are available, model-based analysis, design and testing methods for Hardware–in-the-Loop (HiL) simulation in context of developing motor control functions in automotive applications can be applied. For Hardware–in-the-Loop (HiL) simulation, a high-precision model is required. In this paper, a clustering-based identification method for piecewise-affine (PWA) models for systems with friction is presented that utilizes open-loop recorded data. The method is demonstrated with two industrial electro-mechanical throttles.

Keywords: Vibration and Modal Analysis, Mechanical and Aerospace, Grey Box Modelling
Abstract: We previously proposed a multivariable identification method, called "decoupling identification method", for a horizontal two-link robot arm with elastic harmonic drive gears. This paper extends the identification method to a vertical two-link robot arm with the harmonic drive gears and timing belts, under gravity. The mechanical resonance effects of the timing belts in the high frequency range are decimated in advance, to apply the decoupling method. The characteristics of the timing belts are independently estimated as perturbations in the high frequency range for robust controller design. The effectiveness of the extended identification method was experimentally verified using the vertical two-link robot with the elastic elements.

Keywords: Mechanical and Aerospace, Nonlinear System Identification, Time Series
Abstract: The Airborne Wind Energy paradigm proposes to generate energy by flying a tethered aircraft across the wind flow. Accurate models for tethered flight are essential for the control and optimization of airborne wind energy systems. This paper proposes an estimation of the aerodynamic roll damping of a tethered aircraft based on Inertial Measurement Unit data only, gathered at a high aircraft angular velocity. The resulting system dynamics are nonlinear and the estimation problem is non-convex. Because the aircraft is subject to disturbances, the perturbations are estimated alongside the uncertain parameters. In order to handle the unstable aircraft dynamics, a discretization of the model equations based on multiple-shooting is proposed.

Keywords: Frequency Domain Identification, Mechanical and Aerospace, Recursive Identification
Abstract: Performing tests on complicated systems can be very expensive and having a good model that describes the true system well can significantly reduce cost. This is certainly true for testing of a highly maneuverable fighter aircraft. A real-time method could be useful during testing to help in the decision process for safety reasons and for monitoring the amount of excitation in the collected data, and thus making good post-flight model identification possible. Here, an existing frequency domain method is described and improvements, using the correct finite Fourier transformation of the system equations together with an Instrumental Variable approach to handle atmospheric turbulence as system noise, are suggested. Results from simulations as well as real flight tests are presented.

Keywords: Mechanical and Aerospace, Model Validation, Nonlinear System Identification
Abstract: Identification methodologies for processing flight data are frequently used to validate and improve a pre-flight aerodynamic data-base and, specifically, to reduce the associated uncertainties. This paper describes the process applied for the identification of the aerodynamic model of the Italian Unmanned Space Vehicle. The identification problem is solved through a multi-step approach, where the aerodynamic coefficients are identified first and, in a following phase, a set of model parameters are updated. The methodology was applied to actual flight data, gathered during the second flight test performed by the Italian Aerospace Research Centre.

Keywords: Frequency Domain Identification, Biological Systems, Time Series
Abstract: This paper presents a theoretical basis for linking the anatomical structure, the values of the fractional order model of the impedance and the values of the fractal dimension extracted from time domain respiratory signal analysis. We employ an electrical ladder network model of the lungs which incorporates their specific morphology and anatomical structure. Measurements of 14 healthy volunteers have been used to provide the respiratory input impedance values using the forced oscillation lung function test. The results indicate that the recurrent ladder network model captures well the impedance in the 7-250Hz frequency interval. Next, we show that the time signals of the respiratory system are coupled to the recurrent ladder network values through the fractal dimension parameter evaluated from pressure-volume loops.

Keywords: Biological Systems, Hybrid and Distributed System Identification
Abstract: In this paper, a complete methodology is presented to determine a hybrid model for lung palpation. Specific experiments performed on a mock-up for the lung allow one to record suitable data in order to indentify a viscoelastic model for this organ. The latter is made of a combination of "standard linear solids". Both compression and shear movements are characterized. Next, a two state hybrid model including a contact state and a distension state is deduced to reproduce the behavior of the lung upon palpation. The implementations of the model in simulation and on a haptic device give realistic reaction forces both in compression and in shear for a palpation task.

Keywords: Biological Systems
Abstract: The objective of this study is to better understand and model the effect of dairy matrix structure on the hydrolysis and transit rates of milk proteins during digestion. 2 dairy matrices having a similar composition but differing by their internal structure were manufactured: one solution and one acid gel which both contained a small amount of Cr-EDTA complex, a non-absorbable and non-hydrolysable water soluble marker. These matrices were given to six adult mini-pigs and, for each experiment, 9 samples were collected after the pylori,i.e. at the stomach exit. The first sample was collected before the meal and the 8 others at different times after the meal ingestion. Effluents were analysed to determine their residual concentration in milk proteins (-lactoglobulin and caseins) and the Cr2+ concentration. A mathematical model describing the gastric emptying of Cr-EDTA and these proteins, as well as hydrolysis for proteins, is presented. This model provides a good fitting of the Cr-EDTA and proteins concentrations and allows estimating several unknown digestion parameters with a good accuracy.

Keywords: Biological Systems, Identifiability, Model Validation
Abstract: A simple mass balance model has been developed and tested on lettuce data. A water balance was included in order to predict important fluxes (transpiration, water uptake, etc.) and to consider interactions between the water variables and the metabolism of the plant. A two-stage approach, in which a unique set of yield constants were identified for each stage, was successful in predicting water uptake, carbon dioxide and oxygen concentrations, and final biomass dry weight.

Keywords: Process Control, Nonlinear System Identification, Continuous Time System Estimation
Abstract: This paper deals with the identification of a wastewater treatment pilot process by catalytic ozonation. In general, catalytic ozonation processes operate with a deliberate ozone overproduction to obtain a treated water which respects the discharge standards. But, in this case, the oxygen consumption is not optimal and the operating costs are important. The final objective of this study focuses on the optimization of the catalytic ozonation reactor. The first step, the system identification, is described in this paper. A one-input two-output model is identified to represent the pilot process behavior. The first output is modeled by a nonlinear continuous-time Wiener model, and the second one is given by a linear continuous-time transfer function.

Keywords: Model Validation, Other
Abstract: In this paper we present a new approach to model river systems. In general the dynamics of a single reach can be described with the Saint-Venant equations. These equations can be combined with nonlinear gate equations to fully characterize the behavior of river systems with multiple reaches. Simulating the dynamics of a river system while taking all these nonlinearities into account, can take a lot of time. The complete linearization of these equations can drastically decrease the computational burden on one hand, but on the other hand it can compromise the accuracy of the results. Therefore in this paper we propose to combine the linear version of the Saint-Venant equations with the nonlinear gate equations in order to reduce the computational load while generating accurate results. In addition, we show that the use of Proper Orthogonal Decomposition (POD) and Galerkin Projection can lead to an extra computational saving.

Keywords: Identification for Control, Mechanical and Aerospace, Bounded Error Identification
Abstract: Continuously variable transmissions (CVT) require a feedback controller to reach a targeted transmission speed ratio by commanding pressures on moveable sheaves. The implementation of two on-line identification algorithms are presented to improve the performances and the robutness of the CVT. To compensate for the slow drift of the electro-hydraulic valves during the warm-up period of the transmission, an adaptive feedforward strategy is implemented with the Dasgupta-Huang Outer Bounding Ellipsoid (DHOBE); because of highly correlated input data, a regularization procedure is added, giving the rDHOBE. To compensate for the effect of wear on the pulleys, an improved feedback linearization design is proposed with an on-line adaption of the main nonlinear map in a neural associative memory. The adaptation is required because the stability condition of the feedback controller depends of the accuracy of one of the estimated non-linear maps. The experiments show clear advantages for such adaptive controls over non-adaptive ones.

Keywords: Identification for Control, Input and Excitation Design
Abstract: In recent years, noniterative Correlation-based Tuning (CbT) and Virtual Reference Feedback Tuning (VRFT) have been proposed as an alternative to the standard model-based approach for model-reference control design. In this work, the problem of input design for direct data-driven controller tuning methods is investigated. For bounded input energy, the excitation signal is designed such that the bias on the expectation of the control criterion is reduced. The above strategy is numerically tested on a benchmark example.

Keywords: Identification for Control
Abstract: The recently developed L1 adaptive control theory is a promising approach to robust adaptive control. Due to the specific architecture used in L1 adaptive controllers, robustness and adaptation are separated. High adaptation gains do not affect robustness because the input signal is limited by a low-pass filter and adaptation only occurs within the bandwidth of the system. The approach was initially developed for state feedback control. In this paper, the extension of the approach to output feedback controllers is analyzed and it is concluded that the current output feedback scheme does not provide adaptation. An equivalent LTI controller can be formulated for both output feedback approaches described in Hovakimyan and Cao [2010]. It is shown that for a specific choice of filters commonly used in applications, the equivalent LTI controller is a proportional-integral controller.

Keywords: Identification for Control, Error Quantification, Closed Loop Identification
Abstract: This paper studies a one-shot (non-iterative) data-based method for Model Reference (MR) control design. It shows that the optimal controller can be obtained as the solution of a Prediction Error (PE) identification problem that directly estimates the controller parameters through a reparametrization of the input-output model. The standard tools of PE Identification can thus be used to analyze the statistical properties (bias and variance) of the estimated controller. It also shows that, for MR control design, direct and indirect data-based methods are essentially equivalent.

Keywords: Identification for Control, Process Control, Other
Abstract: Two representative approaches for MRI (MPC Relevant Identification) methods are reported in the literature. The first one is based on the solution of an optimal problem, while the second is based on the prefiltering of the system input and output signals. Each method has advantages and disadvantages in accordance with the process to identify, the length of the prediction horizon or its mathematical implementation. A new MRI method is proposed herein, based on the advantages of both algorithms. A comparison is performed among some MRI methods and the new proposed one. The results indicate that in the studied case, the performance of the new method is better.

Keywords: Grey Box Modelling, Mechanical and Aerospace, Machine Learning and Data Mining
Abstract: This paper investigates the on-line design of nonlinear model predictive control by the use of Kriging as a surrogate model for optimization. This representation is able to address various optimization problems at a very reduced computational cost. It is thus advocated here to deal with nonlinear models in the context of NMPC. One of the main objectives is to assess whether this strategy may be processed in real-time, while ensuring accurate control. An application to the guidance law design of an unmanned aerial vehicle is reported to illustrate the resulting performance.

Keywords: Recursive Identification, Nonlinear System Identification
Abstract: A convergence analysis is performed for a recursive prediction error algorithm discretised using the midpoint integration method. Several conditions are formulated such that the stability of an associated differential equation can be tied to the local and global convergence properties of the algorithm. This shows that convergence to the true parameters is possible. The theoretical analysis of this paper is complemented by numerical example.

Keywords: Recursive Identification
Abstract: A new algorithm for simultaneous online identification of unknown time delay and parameters of discrete-time delay systems is proposed in this paper. This algorithm consists in constructing a linear-parameters formulation and using the recursive least squares approach to solve the obtained system. Simulation example and experimental test results are presented to illustrate the performance of the proposed approach.

Keywords: Recursive Identification, Subspace Methods, Nonlinear System Identification
Abstract: In this paper, the recursive subspace method for Wiener systems with general nonlinearity is considered. By the recursive method for the principle component analysis, the subspace of extended controllability matrix is recursively obtained. Then the matrix coefficients of the linear subsystem and the nonlinear function are also recursively estimated. Under rather mild conditions, all estimates are shown to be consistent. A simulation example is provided justifying the method proposed in the paper.

Keywords: Continuous Time System Estimation, Recursive Identification
Abstract: Conventional adaptive systems algorithms require persistent excitation (p.e.) for exponential convergence, in turn important for robustness. A recently proposed algorithm for localizing a target by a moving agent that can measure its distance from the target, reduces to the same error model. In this case persistent excitation requires the agent’s velocity vector to be p.e.. Yet in many control tasks e.g. where an agent must dock on a target at an unknown location, by measuring its distance from the target, such a p.e. condition cannot be met. In this paper we propose a notion of an excitation condition where the degree of p.e. declines with the quality of estimate and prove uniform asymptotic convergence under this condition.

Keywords: Nonlinear System Identification, Recursive Identification, Nonparametric Methods
Abstract: In this work, we propose a recursive local linear estimator (RLLE) for identification of nonlinear autoregressive systems with exogenous inputs, along with an analysis of its strong consistency and asymptotical mean square error properties. The performance of the proposed RLLE is verified by a simulation example.

Keywords: Recursive Identification, Filtering and Smoothing
Abstract: Kalman filter tuning is based on the process and measurement noise covariances that are often obtained by ad hoc methods. After the filter is tuned, it is necessary to evaluate the quality of the state estimation. In this article, several methods are described for the quality evaluation of the Kalman filter performance. The article includes simulation results evaluating the reliability of the described optimality tests. The sequential test is then used for an adaptive algorithm for a Kalman filter. Further, properties of an autocorrelation function are discussed and several methods for its estimation are compared.

Keywords: Others, Identification for Control, Process Control
Abstract: This paper describes an Interactive Tool for Control Relevant Identification (ITCRI). It evaluates all stages of a control-relevant identification process, from input design to closed-loop control, simultaneously and interactively in one screen. Control-relevance in ITCRI is accomplished primarily through prefiltering, which is implemented via single-pass and two-step algorithms. By simultaneously displaying both open- and closed-loop responses of the estimated models and important control-relevant validation criteria, ITCRI enables the user to readily assess how design variable choices and control performance requirements impact model error and ultimately, closed-loop performance. A case study involving a fluidized bed calciner is presented to illustrate the workings of the tool and the considerations that arise when control requirements are incorporated during identification.

Keywords: Toolboxes, Input and Excitation Design
Abstract: MOOSE is a model based optimal input design toolbox developed for Matlab. The objective of the toolbox is to simplify the implementation of some optimal input design problems encountered in system identification. MOOSE provides an extra layer between the user and a convex optimization environment.

Keywords: Toolboxes
Abstract: In this contribution we provide a status report for the Mathematica toolbox that is described in Sjöberg 2008. The toolbox covers a comprehensive set of functions for handling deterministic and stochastic signals and models. On top of this the toolbox provides signal processing and system identification methods ranging from non-parametric to parametric, and from linear models to a wide class of non-linear models. Algorithms are tailored to be able to efficiently handle large scale data sets and models as well as symbolic computations. This allows theory to be handled alongside practice, implying that the toolbox provides an environment suitable both for education and data processing. In regards to system identification, one of the novel features is graphical support for building block-based nonlinear models. Another novel feature is that modeling errors can be propagated through applications.

Keywords: Neural Networks, Toolboxes, Bayesian Methods
Abstract: In this paper we present a toolbox enabling easy evaluation and comparison of different filtering algorithms. The toolbox is called Kalmtool and is a set of MATLAB tools for state estimation of nonlinear systems. The toolbox now contains functions for Artificial Neural Network Based State Estimation as well as for DD1 filter and the DD2 filter, as well as functions for Unscented Kalman filters and several versions of particle filters. The toolbox requires MATLAB version 7, but no additional toolboxes are required.

Keywords: Toolboxes, Continuous Time System Estimation
Abstract: This paper describes the latest developments for the CONtinuous-Time System IDentification (CONTSID) toolbox to be run with Matlab. The toolbox supports time-domain identification methods for estimating continuous-time linear and nonlinear models directly from regularly or irregularly sampled data. It now includes additional routines for identifying continuous-time linear models in closed loop, as well as efficient routines for identifying both LPV and Hammerstein-Wiener continuous-time models.

Keywords: Identifiability
Abstract: The recent exponential growth in data collection and actuation capabilities has the potential to profoundly impact society, with benefits ranging from safer, self aware environments, to enhanced image-based therapies. A major road-block in realizing this potential stems from the curse of dimensionality. Simply put, existing techniques are ill-equipped to analyze the extremely large volumes of data generated by the sensors. The goal of this paper is to show how the use of simple dynamical systems concepts can lead to tractable, computationally efficient algorithms for robustly extracting information sparsely encoded in extremely large dynamic data sets, a necessary first step in decision making.

Keywords: Nonlinear System Identification, Neural Networks, Grey Box Modelling
Abstract: A comparison of the POLYnomial MOdel Tree (POLYMOT) and the HIerarchical LOcal MOdel Tree (HILOMOT) algorithm for the construction of local model networks is presented in this paper. A comprehensive benchmark study with different 2-dimensional test functions as well as four popular measured datasets demonstrates the robustness against noise and overfitting of both algorithms. The major number of axes-oblique local linear models by using HILOMOT is often compensated by a smaller number of more complex axes-orthogonal local polynomial models by using POLYMOT, so that both methods generate the same model quality. However, for high-dimensional input spaces HILOMOT demonstrates its advantage of axis-oblique partitioning.

Keywords: Nonlinear System Identification, Nonparametric Methods
Abstract: The estimation of nonlinear functions can be challenging when the number of independent variables is high. This difficulty may, in certain cases, be reduced by first projecting the independent variables on a lower dimensional subspace before estimating the nonlinearity. In this paper, a statistical nonparametric dimension reduction method called sliced inverse regression is presented and a consistency analysis for dynamically dependent variables is given. The straightforward system identification application is the estimation of the number of linear subsystems in a Wiener class system and their corresponding impulse response.

Keywords: Nonlinear System Identification, Model Validation, Process Control
Abstract: The use of surrogate data for nonlinear identification is illustrated using a case study. It is shown how the surrogate data approach can be used to detect nonlinear features in the experimental data, and how this approach can be used to determine whether a model is insufficient for describing the detected nonlinear predictability. In order to develop a nonlinear model, the structure of an identified continuous time linear model is used. The developed continuous time nonlinear models are then evaluated, and some deemed adequate for capturing the nonlinear predictability of the data.

Keywords: Nonlinear System Identification, Identification for Control
Abstract: Here we deal with the choice of the sampling rate in nonlinear system identification applications. In particular, we focus on the effect of the sampling rate when the prediction-error method is used. On one hand, a high sampling rate is advantageous since it enables the measurement of high-frequent nonlinear components in the output signal of the system without aliasing. However, a high sampling rate might also make it harder to realize that the system is nonlinear, since the nonlinearities cannot be detected in the residuals from a linear model in some cases. Here, this phenomenon is illustrated in a couple of numerical examples and a way to avoid it is proposed.

Keywords: Recursive Identification, Nonlinear System Identification
Abstract: This paper deals with studying the asymptotical properties of neural networks used for the adaptive identification of nonlinearly parameterized system. To update the neural network’s parameters, simple online gradient type learning algorithm is employed. A distinguishing feature of this algorithm is that its step size remains constant both in non-stochastic case and in stochastic case, and the learning set is infinite. Based on the Lyapunov-like concept, sufficient conditions guaranteeing the convergence of the learning algorithms are derived. Simulations are presented to support the theoretical results.

Keywords: Nonlinear System Identification, Grey Box Modelling, Identification for Control
Abstract: The article deals with the stability constraint in nonlinear continuous-time dynamic model identification. The identification is formulated as a boundary value problem. Constraining the norm of the terminal sensitivity to the initial condition is used to drive the model state to a stable equilibrium. Solving such boundary value problem on an extending finite time horizon may be numerically more appealing than constraining the eigenvalues of the Jacobian matrix evaluated at the equilibrium point in the state space.

Keywords: Input and Excitation Design, Frequency Domain Identification, Nonlinear System Identification
Abstract: This paper discusses the design, implementation and the advantages of three types of signals for nonlinear system analysis and identification. They belong to the class of multisine signals and are the random phase, positively skewed and crest factor optimised multisine signals. A straightforward routine to combine such a signal with the system's typical input signal is discussed. The advantages of using such signals is illustrated through the results obtained from identifying the dynamics of a mechanical wet-clutch system.

Keywords: Input and Excitation Design
Abstract: Optimal input design typically depends on the unknown system parameters that need to be identified. In this paper we consider robust input design for resonant systems that may span over a large frequency band. The concept is to use classical D-optimal design combined with a robust excitation signal which guarantees the same estimate variance regardless of resonance frequency. Simulations show that the proposed signal has the desired properties.

Keywords: Input and Excitation Design, Biological Systems
Abstract: This paper extends recent work on amplitude-constrained experiment design with a new strategy for finding feasible solutions based on convex relaxation, randomization, and a new iterative strategy. The method is applied to an important problem in neurological diagnosis: estimating the parameters of the cerebrospinal fluid system. A craniospinal fluid infusion pattern must designed which generates optimal information about these parameters, subject to strict safety constraints.

Keywords: Multivariable System Identification, Identifiability, Input and Excitation Design
Abstract: Structure identification of large-scale but sparse-flow interconnected dynamical systems from limited data has recently gained much attention in the control and signal processing communities. This paper reviews some of the recent results on Compressive Topology Identification (CTI) of such systems with a particular focus on sufficient recovery conditions. We list and discuss the key elements that influence the recovery performance of CTI, namely, the network topology, the number of measurements, and the input sequence. In regards to the last element, we analyze the recovery conditions with respect to an experiment design.

Keywords: Input and Excitation Design, Maximum Likelihood Methods
Abstract: This work solves an experiment design problem for a linear regression problem using a reduced order model. The quality of the model is assessed using a mean square error measure that depends linearly on the parameters. The designed input signal ensures a predefined quality of the model while minimizing the input energy.

Keywords: Input and Excitation Design
Abstract: In this paper, the problem of input signal design with the property that the estimated model satisfies a given performance level with a prescribed probability is studied. The aforementioned performance level is associated with a particular application. This problem is well-known to fall within the class of chance-constrained optimization problems, which are nonconvex in most cases. Convexification is attempted based on a Markov inequality, leading to semidefinite programming (SDP) relaxation formulations. As applications, we focus on the identification of multiple input multiple output (MIMO) wireless communication channel models for minimum mean square error (MMSE) channel equalization and zero-forcing (ZF) precoding.

Keywords: Errors in Variables Identification, Continuous Time System Estimation
Abstract: This paper deals with continuous-time system identification with fractional models in Errors-In-Variables context. Two estimators based on Higher-Order Statistics (third-order cumulants) are proposed. A State Variable Filter approach is extended to fractional orders to compute fractional derivatives of third-order cumulants estimates. The performance of the proposed algorithms is illustrated in a numerical example. Firstly, differentiation orders are fixed and differential equation coefficients are estimated. The consistency of the proposed estimators is evaluated through a study of the tuning parameter and Monte Carlo simulations. Then, the commensurate differentiation order is optimized along with the differential equation coefficients.

Keywords: Errors in Variables Identification, Multivariable System Identification
Abstract: This paper deals with the identification of multi–input multi–output errors–in–variables (EIV) models in the Frisch scheme context. The extension of the Frisch scheme to MIMO models introduces some problems not present in the SISO case. The approach proposed in this paper relies on the association of EIV models to directions in the noise space and on the statistical properties of the residual of the EIV model. In particular, a selection criterion based on the comparison of the theoretical statistical properties of the residual with those computed from the data is introduced. The performance of the proposed identification algorithm is evaluated by means of numerical simulations.

Keywords: Errors in Variables Identification, Identifiability
Abstract: Some tests for model order determination based on reduced rank of cross-covariance matrices are reviewed and examined. Applications for errors-in-variables problems are particularly discussed. Tests based on the smallest singular values of the sample cross-covariance matrix are developed.

Keywords: Mechanical and Aerospace, Closed Loop Identification
Abstract: This paper deals with the topic of robots dynamics identification. In this paper, we focus on the instrumental variable (IV) technique. For robots, the set of instruments is the inverse dynamic model built from simulated data which are calculated from the integration of the direct dynamic model, assuming the same reference trajectories and the same control law structure for both actual and simulated robots. The integration of the direct dynamic model is based on previous IV estimates. This defines an iterative algorithm. Furthermore, gains of the simulated controller are updated to get a fast convergence. Experimental results obtained on a six degrees of freedom robot manufactured by Stäubli show the effectiveness of our approach: 60 dynamic parameters are estimated in only two iterations.

Keywords: Mechanical and Aerospace, Closed Loop Identification, Subspace Methods
Abstract: This paper reports the experimental results of the dynamic modelling using MIMO closed-loop system identification, controller design and implementation for hovering flight of a coaxial radio-controlled helicopter. The helicopter is set on our handcrafted supporting device, and it has the roll, side-to-side and up-and-down motions. The maneuvers are done by the aileron and the throttle. Hence, our system is with 2 inputs and 3 outputs. A dynamic model is derived for hovering flight conditions from closed-loop system identification experiments with the MOESP-type closed-loop subspace model identification method (CL-MOESP). Then, an LQR with a full state observer is designed and implemented.

Keywords: Identification for Control, Closed Loop Identification, Nonlinear System Identification
Abstract: An algebraic framework is developed and utilized to achieve adaptive control of asynchronous sequential machines with unknown transitions. The framework yields adaptive state feedback controllers that acquire data about unknown transitions during normal operation and utilize this data to improve closed-loop performance.

Keywords: Other, Multivariable System Identification, Nonlinear System Identification
Abstract: Wind turbines in a wind farm, influence each other through the wind flow. Downwind turbines are in the wake of upwind turbines and the wind speed experienced at downwind turbines is hence a function of the wind speeds at upwind turbines but also the momentum extracted from the wind by the upwind turbine. This paper establishes flow models relating the wind speeds at turbines in a farm. So far, research in this area has been mainly based on first principles static models and the data driven modelling done has not included the loading of the upwind turbine and its impact on the wind speed downwind. This paper is the first where modern commercial mega watt turbines are used for data driven modelling including the upwind turbine loading by changing power reference. Obtaining the necessary data is difficult and data is therefore limited. A simple dynamic extension to the Jensen wake model is tested without much success. The best model turns out to be non linear with upwind turbine loading and wind speed as inputs. Using a transformation of these inputs it is possible to obtain a linear model and use well proven system identification methods. Finally it is shown that including the upwind wind direction to explain the wake improve the prediction performance.

Keywords: Identification for Control, Other, Recursive Identification
Abstract: Grid integration of wind power, especially using offshore wind farms, is dramatically increasing all over the world. Consequently, the reliability and robustness of wind turbines against faults are becoming important issues these days. In this paper, a new wind turbine Fault Tolerant Control (FTC) strategy based on adaptive Subspace Predictive Control (SPC) is proposed. The proposed strategy uses a model predictive control algorithm with its predictor matrices continuously updated using recursive subspace identification techniques. In contrast with SPC algorithms previously proposed in the literature, the proposed strategy includes integral action, and consequently, offers better disturbance rejection and better performance. The effectiveness of the proposed strategy is illustrated using detailed simulations of a 1.5 MW variable-speed variable-pitch wind turbine model with a fault in the hydraulic pitch system.

Keywords: Other
Abstract: The purpose of this paper is to present the application of interval LPV identification and fault diagnosis approaches to a real wind turbine. Since wind turbines are highly non-linear systems when operating in their whole range of operation, a Linear Parameter Varying (LPV) model is used. Real field data and system identification techniques are used to identify the nominal model as well as its uncertainty. Fault detection is based on interval LPV observers that are used to generate an adaptive threshold to enhance the robustness of the fault detection test. Finally, fault isolation is based on an algorithm that uses the residual fault sensitivity. Several fault scenarios are used to show the performance of the proposed approach.

Keywords: Mechanical and Aerospace, Grey Box Modelling, Continuous Time System Estimation
Abstract: This paper addresses the measurement of the wheel angular velocity of wheeled vehicles. The wheel angular velocity measurement is often affected by large periodic disturbances. The paper proposes a model of the origin of that disturbance: even a small offset in the positioning of the encoder can cause large, velocity dependent noise. After having shown that the periodic term is indeed a noise and not part of the actual signal, an adaptive notch filter is discussed. Lyapunov theory is employed to prove the quadratic stability of the time-variant filter. An analysis of both simulation and experimental tests supports the analysis and methods.

Keywords: Mechanical and Aerospace, Continuous Time System Estimation, Filtering and Smoothing
Abstract: Vehicle dynamics control systems are becoming available for single-track vehicles. The dynamics of single-track vehicles have some unique features that require ad hoc solutions. One of the most critical aspects is the estimation of the vehicle body velocity. In this paper the problem of estimating the body velocity of a two wheeled vehicle for traction control applications is discussed. The front wheel velocity and the longitudinal acceleration measurements are used to estimate the vehicle velocity according to a sensor fusion philosophy. The complementary filter approach is compared against a more advanced Kalman filter. It is shown that the mentioned Kalman filter can be written as a second order complementary filter; this allows to derive quantitative guidelines for the tuning of the filter. The proposed methods are shown to be more robust to wheelies than the front wheel velocity based estimate. Experimental tests on an instrumented bike validate the methods for traction control applications.

Keywords: Mechanical and Aerospace, Model Validation, Errors in Variables Identification
Abstract: A challenging topic in the eld of planetary rover simulations is the modeling of the contact between the rover and its environment. Multibody simulation models are used to represent the kinematic structure of a wheeled rover, but its interface with the environment relies on sand-wheel contact dynamics. A new advanced contact model is presented and tuned according to single wheel experiments by comparison between experimental data and predicted values. Finally, stochastic model updating is performed to assess parameter uncertainty level due to soil properties. As a result, the mean percentage error of the tuned model is inside the acceptable range, but additional improvements in the rover sinkage computation model are still desired.

Keywords: Biological Systems, Nonlinear System Identification
Abstract: One key challenge in systems biology is to develop theoretical methods that enable the identification of kinetic models from limited quantitative data. In this work, we illustrate the potential of Chemical Reaction Network Theory for model identification of kinetic models, setting up the basis for a novel method for inverse bifurcation analysis of bistable biochemical systems. Inverse bifurcation analysis aims to determine values of model parameters that result in certain desired properties of the underlying bifurcation diagrams. The method presented here exploits the structural properties of chemical networks -described by the Chemical Reaction Network Theory (CRNT)- to infer the kinetic parameters from dose response curves. In this way, it allows to drastically reduce the feasible regions in the parameter space, improving identifiability and facilitating the parameter estimation task in combination with standard approaches.

Keywords: Identifiability, Biological Systems
Abstract: Parameter estimation from experimental data is a crucial problem in quantitative modeling of biochemical reaction networks. An especially important issue, raised by the complexity of the models and the challenging nature of the experimental data, is parameter identifiability. Despite several approaches proposed in the systems biology literature, no agreement exists on the analysis of structural and practical identifiability, and the relations among the two. In this paper we propose a mathematical framework for the analysis of identifiability of metabolic network models, establish basic results and methods for the structural and practical identifiability analysis of the class of so-called linlog models, and discuss the results on the basis of an artificial example.

Keywords: Nonlinear System Identification, Biological Systems, Time Series
Abstract: This paper deals with the reconstruction of the interaction structure of a gene regulation network from qualitative data in a Boolean framework. The problem in this setup is to find update functions which are in agreement with the data. As the search space grows exponentially with the system size but data are rare, large uncertainties remain in the reconstructed networks. In order to attenuate this problem, we propose to restrict the search space to the biologically meaningful class of unate functions. Using sign-representations, the problem of exploring this reduced search space is transformed into a linear feasibility problem. The sign-representation furthermore allows to incorporate robustness considerations and gives rise to a new measure which can be used to further reduce the uncertainties. The proposed methodology is demonstrated with a Boolean apoptosis signaling model.

Keywords: Nonlinear System Identification, Biological Systems, Identifiability
Abstract: Photodynamic therapy (PDT) is an alternative treatment for cancer that involves the administration of a photosensitizing agent, which is activated by light at a specific wavelength. In this project, we aim at developing a model-based approach to compare the in vivo photodynamic efficiencies of different photosentizers. Unfortunately, constraints of in vivo experiments are such that it is impossible to estimate all the photophysical parameters. However in this paper, a feasibility study is performed to (i) select the most relevant model parameters and (ii) estimate their value and their confidence interval. Despite the previously mentioned difficulties, the results obtained in practice from in vivo experiments have shown promising results.

Keywords: Time Series, Biological Systems, Nonlinear System Identification
Abstract: This paper addresses the problem of identifying the main characteristics of Turing patterns by spatial recurrence properties. Changes in patterns shapes and spatial frequencies are estimated by the application of generalized recurrence quantification measures, establishing their relationships with the model parameters. Furthermore, variations of the recurrence measures respect to the spatial frequency are shown to fulfill theoretical results. A comparison with the standard two dimensional Fourier transform is carried out, showing that the recurrence indicators perform better in identifying a reliable connection with the spatial frequency of the patterns.

Keywords: Nonlinear System Identification, Identification for Control, Biological Systems
Abstract: Muscles can be conceived as distributed electro-mechanical-chemical systems that can be described by a set of coupled partial differential equations. Because of the difficulty of solving this kind of equations, these systems are usually approximated by a set of lumped elements leading to a set of coupled ordinary differential equations instead. Hill's model is the most popular of such models having four basic elements that describe the behavior of the muscle: contractile, damping, series elastic, and parallel elastic elements. The aim of this paper is to study the effects of introducing fractional dynamics into the Hill's model in order to characterize unhealthy muscles in spinal cord injured (SCI) subjects for control purposes. By doing so, more general dynamic behaviors can be obtained but keeping the simplicity of the lumped parameter models for control applications.

Keywords: Subspace Methods, Nonlinear System Identification
Abstract: This paper presents a Basis Pursuit DeNoising (BPDN) sparse estimation approach as a regularization technique in a predictor-based subspace method for the identification of Linear Parameter-Varying (LPV) state-space systems. It is known that in this identification method, the choice of the past window of a state predictor factorization will influence the conditioning of the main parameter estimation problem. Therefore, prior knowledge of the system order may be needed to choose the past window in such a way that this problem is well-conditioned. It will be demonstrated that sparse estimation through BPDN can reduce the sensitivity of the conditioning with respect to the past window parameter. In this way, we can simplify the task of choosing the past window to an extend that the need for prior knowledge of the system order is eliminated. Also, this paper will pay attention to the synthesis of stabilizing observer gain matrices in the identified LPV innovation-type state-space model.

Keywords: Nonlinear System Identification, Subspace Methods, Other
Abstract: We address the identification of discrete-time linear parameter varying systems in the state-space form with affine parameter dependence. In previous work, some of the authors have addressed this problem and an iterative algorithm that avoids the curse of dimensionality, inherent to this class of problems, was developed for the identification of multiple input multiple output systems. Although convergence of this algorithm has been assured for white noise sequences, it has also converged for other type of scheduling signals. Neverless, its application is still not generalized to every class of scheduling parameters. In this paper, the algorithm is modified in order to identify multiple input single output systems with quasi-stationary scheduling signals. In every iteration, the system is modeled as a linear time invariant system driven by an extended input composed by the measured input, the Kronecker product between this signal and the scheduling parameter and the Kronecker product between the scheduling and the state estimated at the previous iteration. The remaining unknown signals are considered as “noise”. Furthermore, the system is decomposed into a “deterministic” system driven by the known inputs and a “stochastic” subsystem driven by noise. The system is identified as a high order autoregressive exogeneous model. In order to whiten the noise, the input/output data is filtered by the inverse noise transfer function and a state-space model is estimated for the “deterministic” subsystem. Then, the output simulated by this system is subtracted from the measurements to obtain the output stochastic component. Finally, the state of the system is estimated using a Kalman filter and a deconvolution technique. Then, the state becomes an entry to the system for the next iteration, after being multiplied by the scheduling parameter. The whole process is repeated until convergence. The algorithm is tested using periodic scheduling signals and compared with other approaches developed by the same authors.

Keywords: Nonlinear System Identification, Nonparametric Methods, Machine Learning and Data Mining
Abstract: Abstract: Parametric identification approaches in the Linear Parameter-Varying (LPV) setting require optimal prior selection of a set of functional dependencies, used in the parametrization of the model coefficients, to provide accurate model estimates of the underlying system. Consequently, data-driven estimation of these functional dependencies has a paramount importance, especially when very limited a priori knowledge is available. Existing overparametrization and nonparametric methods dedicated to nonlinear estimation offer interesting starting points for this problem, but need reformulation to be applied in the LPV setting. Moreover, most of these approaches are developed under quite restrictive auto-regressive noise assumptions. In this paper, a nonparametric Least-Squares Support Vector Machine (LS-SVM) approach is extended for the identification of LPV polynomial models. The efficiency of the approach in the considered noise setting is shown, but the drawback of the auto-regressive noise assumption is also demonstrated by a challenging LPV identification example. To preserve the attractive properties of the approach, but to overcome the drawbacks in the estimation of polynomial LPV models in a general noise setting, a recently developed Instrumental Variable(IV)-based extension of the LS-SVM method is applied. The performance of the introduced IV and the original LS-SVM approaches are compared in an identification study of an LPV system with unknown noise dynamics.

Keywords: Nonlinear System Identification
Abstract: The problem of identifying linear parameter-varying (LPV) systems, a-priori known to be quadratically stable, is considered in the paper using an input-output model structure. To solve this problem, a novel constrained optimization-based algorithm is proposed which guarantees quadratic stability of the identified model. It is shown that this estimation objective corresponds to a nonconvex optimization problem, defined by a set of polynomial matrix inequalities (PMI), whose optimal solution can be approximated by means of suitable convex semidefinite relaxations. Applicability of such relaxation-based estimation approach in the presence of either stochastic or deterministic bounded noise is discussed. A simulation example is also given to demonstrate the effectiveness of the resulting identification method.

Keywords: Multivariable System Identification, Frequency Domain Identification
Abstract: This paper presents a State-space Model Interpolation of Local Estimates (SMILE) technique to compute linear parameter-varying (LPV) models for parameter-dependent systems through the interpolation of a set of linear time-invariant (LTI) state-space models obtained for fixed operating conditions. Since the state-space representation of LTI models is not unique, a suitable coherent representation needs to be computed for the local LTI models such that they can be interpolated. In this work, this coherent representation is computed based on observability and controllability properties. It is shown that compared with the state of the art in the literature, this new method has three strong appeals: it is general, fully automatic and results in numerically well-conditioned LPV models. An example demonstrates the potential of the new SMILE technique.

Keywords: Nonlinear System Identification, Process Control, Basis Functions
Abstract: This article presents the identification of a web winding system as an LPV system with the reel radius as the time-varying parameter. This system is non-linear, time-varying and input-output unstable. Two methods are employed: First, an LPV model is estimated in a single step using a novel approach based on sparse identification and Set Membership optimality evaluation. Then, local LTI models are identified using classical identification algorithms and the overall LPV model is constructed as a weighted sum of the local models. The two methods are applied to experimental data measured on a real web winding machine.

Keywords: Recursive Identification, Maximum Likelihood Methods, Particle Filtering/Monte Carlo Methods
Abstract: Parameter estimation in general state space models is not trivial as the likelihood is unknown. We propose a recursive estimator for general state space models, and show that the estimates converge to the true parameters with probability one. The estimates are also asymptotically Cramer-Rao efficient.

The proposed estimator is easy to implement as it only relies on non-linear filtering. This makes the framework flexible as it is easy to tune the implementation to achieve computational efficiency.

This is done by using the approximation of the score function derived from the theory on Iterative Filtering as a building block within the recursive maximum likelihood estimator.

Keywords: Recursive Identification, Continuous Time System Estimation, Vibration and Modal Analysis
Abstract: This paper proposes a method that estimates the parameters of a seismically excited building. The acceleration measurements of the ground and of each floor are used for identification purposes. It is assumed that these measurements have offsets and noise. The proposed scheme is based on the Recursive Least Squares algorithm with forgetting factor and a parametrization of the structure using integrals over finite time intervals. These filters have finite impulse response, pass the typical frequency bandwidth of structures undergoing earthquake excitation, eliminate the offsets in a small finite time and attenuate the measurement noise. To confirm the effectiveness of the proposed method a simulation of a three-story building is presented. The results show that the estimated parameters converge to the true parameters in a short time.

Keywords: Bayesian Methods, Recursive Identification, Continuous Time System Estimation
Abstract: Aiming at survival from contingency situations for unmanned aerial vehicles, a square root spherical simplex unscented Kalman filter is applied for state and parameter estimation and a rough model is used for state prediction when essential measurements are lost. Processing real flight data, received by telemetry at quite low sampling rate, the paper shows that filter performance of reasonable quality can be achieved despite the low sampling rate and the result is a low order model that can be useful during contingency operation. It is shown that the filter-estimator approach can cope with the low rate measurements requirering very little system knowledge and very limited tuning efforts. A generic aircraft model is utilised as process model where the non dimensional coefficients are identified online with joint estimation of states. Numerical stability is guaranteed by mathematically efficient square root implementation of the filter algorithm. A case of loss of GPS signal demonstrates the use of the state estimates to obtain return of the UAV to close to it's home base where safe recovery of the plane is possible.

Keywords: Bayesian Methods
Abstract: Recursive estimation forms core of adaptive prediction and control. Dynamic exponential family is the only but narrow class of parametric models that allows exact Bayesian estimation. The paper provides an approximate estimation of important autoregressive model with exogenous variables (ARX) and uniform noise. This model reflects well physical nature of modelled system: majority of signals, noise and estimated parameters are bounded. Unlike former solutions, the paper proposes an algorithm that provides a full (approximate) posterior probability density function (pdf) of unknown parameters. Behaviour of the designed algorithm is illustrated by simulations.

Keywords: Basis Functions, Input and Excitation Design, Continuous Time System Estimation
Abstract: Preliminary process information is generally based on step tests or on operator experience. Step tests are usually long, poorly informative and sensitive to disturbances during the experiment. A preliminary identification test and the time and the frequency identification techniques are presented in order to obtain the preliminary process information. A combined process model, an OBF model part and a time delay part, named orthonormal basis filter plus time delay (OBF-TD) is proposed. As the time delay is handled separately, the model order can be chosen to improve model performance. In addition to that, it is possible to directly obtain FOPTD models. Simulation results for SISO and MIMO processes are presented to illustrate the techniques.

Keywords: Basis Functions, Identification for Control, Multivariable System Identification
Abstract: In this paper we propose an efficient two-level model identification method for a large class of linear-in-the-parameters models from the observational data. A new elastic net orthogonal forward regression (ENOFR) algorithm is employed at the lower level to carry out simultaneous model selection and elastic net parameter estimation. The two regularization parameters in the elastic net are optimized using a particle swarm optimization (PSO) algorithm at the upper level by minimizing the leave one out (LOO) mean square error (LOOMSE). Illustrative examples are included to demonstrate the effectiveness of the new approaches.

Keywords: Toolboxes, Closed Loop Identification, Subspace Methods
Abstract: The ADAPT-lpv software for the identification of linear parameter-varying (LPV) and/or nonlinear systems is a direct and simple extension of the canonical variate analysis (CVA) method as implemented in the ADAPTx software for identification of linear time-invariant systems. The computational structure and problem size is very similar to ADAPTx except that the matrix row dimension (number of lagged variables of the past) is multiplied by the effective number of parameter-varying functions. This is in contrast with the exponential explosion in the number of variables using current subspace methods for LPV systems. Compared with current methods, initial results indicate much less computation, maximum likelihood accuracy, and better numerical stability. The method can automatically remove a number of redundancies in the nonlinear models producing near minimal state orders and polynomial degrees by hypothesis testing. There is detailed discussion of the computational methods and structure of the software modules. The software is demonstrated on a widely studied aircraft flutter problem.

Keywords: Toolboxes, Continuous Time System Estimation, Multivariable System Identification
Abstract: Version 8.0 of MATLAB's System Identification toolbox is released with version R2012a of MATLAB in the spring of 2012. This release presents a re-engineered implementation of the code using the new MATLAB object-oriented programming. Two main features are (1) that the toolbox commands and plots are seamlessly integrated with the other MATLAB toolboxes that deal with linear dynamic systems and (2) several new features and model objects. The toolbox now supports multi-input--multi-output (MIMO) systems across all model objects, and more emphasis is placed on continuous-time models. Also a new model object, IDTF covers MIMO transfer function models in both continuous and discrete time.

Keywords: Toolboxes, Frequency Domain Identification, Identification for Control
Abstract: The algorithm, the structure and area of application of package "Automatica" are considered. The package is intended for engineers-developers of real-world control system. The purpose of such users is to provide the given tolerance on steady-state error for each controlled variables when the disturbance is unknown but bounded function and the uncertain plant parameters change their values slowly. In this connection, the identification of plant parameters and redesign of controller are required. The package has special structure that is oriented for such users. The basis of this structure is the directives that solve defined class of problems. The package includes three groups of directives: controller design, finite-frequency identification, frequency adaptive control.

Keywords: Toolboxes
Abstract: The paper briefly reviews the main features of the CAPTAIN Toolbox, outlines some recent developments and presents a number of examples that demonstrate the performance of these new routines.

Keywords: Input and Excitation Design, Nonlinear System Identification, Frequency Domain Identification
Abstract: Pseudorandom signals are widely used as input signals for system identification, but they have the drawback that there are many different kinds, each with a sparse range of possible periods. This paper shows how object-oriented concepts can be used in a single MATLAB program to create pseudorandom signals with specified levels and spectral or correlation properties for which very large numbers of periods are available. The signals are suitable for single-input and multi-input system identification, and the program can be used independently or in combination with MATLAB Toolboxes.