Keywords: Adaptive control design, Distributed parameter systems, Stability analysis
Abstract: Gradient extremum seeking for compensating wave actuator dynamics in cascade with static scalar maps is addressed in the present paper. This class of Partial Differential Equations (PDEs) for extremum seeking has not been studied yet. A dynamic feedback control law based on distributed parameters is proposed by employing backstepping transformation with an appropriate target system and an adequate formulation using Neumann interconnections. Local stability and convergence to a small neighborhood of the desired (but unknown) extremum is proved by means of a Lyapunov functional and the theory of averaging in infinite dimensions. Numerical simulations illustrate the theoretical results.

Keywords: Adaptive control design, Linear control design, Performance and robustness analysis
Abstract: This paper deals with a design problem of a decentralized variable gain robust controller via piecewise Lyapunov functions for a class of uncertain large-scale interconnected systems. The decentralized variable gain robust controller developed in this paper consists of fixed gains and compensation inputs tuned by parameter adjustment laws. In this paper, we show LMI-based sufficient conditions for the existence of the decentralized variable gain robust controller. Finally, the effectiveness of the proposed decentralized variable gain robust control system is presented through a simple numerical example.

Keywords: Adaptive control design, Performance and robustness analysis, Nonlinear systems
Abstract: The paper addresses the problem of performance improvement of robust adaptive backstepping control for a class of disturbed nonlinear systems presentable in parametric-strictfeedback form. The proposed solution is based on backstepping procedure reducing to actual control and an error model. Later motivates design of robust σ-modification of adaptation algorithm with improved parameters tuning of the actual control. Tuning improvement is achieved by applying Kreisselmeier’s scheme of adaptation algorithm with memory regressor extension (MRE). MRE is provided by involving a linear filter into adaptation algorithm. On the one hand this filter records the regressor over past period of time (with some forgetting) and, as a result, accelerates the tuning of control. On the other hand the filter allows to generate the higher order time derivatives of adjustable parameters used for calculation of virtual and actual controls. The actual control obtained is robust with respect to disturbance, is free from overparameterization, does not contain tuning functions and completely compensates for nonlinear dynamics together with uncertainties of the plant. The efficiency of proposed solution is demonstrated via simulation.

Keywords: Adaptive control design, Adaptive observers and estimators, Neuro-fuzzy modelling and control
Abstract: This paper explores the development of an LMI design of observer-based output feedback control synthesis of discrete-time nonlinear systems in the form of Takagi-Sugeno (T-S) fuzzy model via adopting a multilateral matrix methodology. Based on our previous results, this paper presents an improved innovated synthesis design solution by introducing a few more of slack matrix variables. This advanced approach is developed further while the relative sizes among different normalized fuzzy weighting functions are utilized via additionally employing certain matrix variables hence its proof has been refined too. Thus, some weak points of the previous synthesis design have been refined and a desired solution is provided reducing some conservatism and computation complexity alleviation. The effectiveness of the proposed innovated approach is demonstrated by means of appropriate examples.

Keywords: Nonlinear control design, Adaptive control design, Adaptive observers and estimators
Abstract: This work presents an adaptive observer-based control strategy for maximum power point tracking (MPPT) of uncertain photovoltaic (PV) systems. On the one hand, the PVG output voltage and/or current measurements are needed for MPPT techniques and controllers design and, on the other hand, the PV arrays have to be installed in a site that profits from good daily sunshine. This obviously leads to difficulty of PVG output current and voltage measurement if ever such a site is at great distance from the converter. Furthermore, the MPPT control accuracy could be significantly affected due to the cable parameters if only voltage and current measurements on the converter side of the cable are instead used. To overcome this issues, an adaptive extended Kalman--like observer providing estimates of PVG output current and voltage regardless of cable resistance and inductance deviations, is first designed. Afterwords, a backstepping controller is synthesized to ensure the MPPT objective. The designed adaptive observer-based MPPT control convergence is formally analyzed and its effectiveness in compensating for cable parameters uncertainties on the MPPT accuracy is validated through numerical simulations.

Keywords: Nonlinear systems, Adaptive control design, Stability analysis
Abstract: In adaptive control it is typically proven that a weak asymptotic form of stability holds; furthermore, at best it is proven that a bounded noise yields a bounded state. Recently, however, it has been proven in a variety of scenarios that it is possible to carry out adaptive control for a linear-time invariant (LTI) discrete-time plant so that the closed-loop system enjoys exponential stability, a bounded gain on the noise, as well as a convolution bound on the effect of the exogenous inputs; the key idea is to carry out parameter estimation by using the ideal projection algorithm in conjunction with restricting the parameter estimates to a convex set. In this paper we extend the approach to a class of first-order nonlinear systems.

Keywords: Identification methods design and analysis, Nonlinear system identification, Open system identification
Abstract: The paper addresses the problem of Hammerstein-Wiener (N-L-N) system identification. The system is identified in so-called two-experiment approach. In passive experiment the system is excited with random noise, whereas in active experiment binary sequences are used. We present an algorithm with four consecutive stages, in which static nonlinear characteristics are recovered separately from the linear dynamic block. The proposed method uses both parametric and nonparametric identification tools. The estimates are based on kernel preselection of data and application of local least squares. Identification of output nonlinearity is processed under active experiment. We analyze the consistency of the proposed estimates under some a priori restrictions imposed on the excitation signal and system characteristics. Finally, we present a simple simulation example to demonstrate the behaviour of the algorithm.

Keywords: Nonlinear system identification, Graphical models and kernel methods
Abstract: In this paper, we present a simulation study to investigate the role of manifold regularization in kernel-based approaches for nonparametric nonlinear SISO (Single-Input Single-Output) system identification. This problem is tackled as the estimation of a static nonlinear function that maps regressors (that contain past values of both input and output of the dynamic system) to the system outputs. Manifold regularization, as opposite to the Tikhonov one, enforces a local smoothing constraint on the estimated function. It is based on the assumption that the regressors lie on a manifold in the regressors space. This manifold is usually approximated with a weighted graph that connects the regressors. The present work analyzes the performance of kernel-based methods estimates when different choices are made for the graph connections and their respective weights. The approach is tested on benchmark nonlinear systems models, for different connections and weights strategies. Results give an intuition about the most promising choices in order to adopt manifold regularization for system identification.

Keywords: Nonlinear system identification, Identification methods design and analysis, Nonlinear systems
Abstract: Identification of nonlinear systems is presented using a neural network variant known as the temporal convolutional network (TCN). The identification capabilities of TCNs and standard feedforward neural networks (FNNs) are benchmarked and compared using the Silverbox dataset: a publicly available dataset from a circuit equivalent to a nonlinear spring-mass damper. The TCN is found to have superior performance in simulation of the test portion of the dataset. In addition, published benchmark results are surveyed and compared to the TCN results. Analysis of existing results reveals testing variances that effect model performance, so guidelines for fair comparison of models on the Silverbox benchmark are presented.

Keywords: Nonlinear system identification, Intelligent learning in control systems, Industrial processes & manufacturing
Abstract: Advanced learning methods enable the model-based control of systems with complex unknown dependencies. Within the German cluster of excellence "Internet of Production", a configuration for an interconnected data-base is proposed, where data-driven model-based control strategies can be applied using the collective knowledge and adapted online according to data. For the exchanged data it is imperative to establish a generalizing learning technique for the controller design. A machine learning technique with inherent generalization ability is the Support Vector Machines (SVM) algorithm, where the choice of kernel is crucial for the resulting model quality. In the related literature, usually a radial basis function (RBF) is chosen as kernel, although many studies show the necessity of a more sophisticated kernel selection. This work tackles the point of a kernel selection based on composite kernel search in context of data-driven model-based control of a CNC machining center. The results support the capability of the presented approach to further automate and improve the identification of the controller model for the machining center.

Keywords: Nonlinear system identification, Learning theory and algorithms, Power & energy systems
Abstract: Combustion Rate Shaping (CRS) offers the potential to control in-cylinder fuel concentration gradient and distribution with new fuel injection strategies, consisting of a higher numbers of injections and smaller individual injection quantities. Developing a physics-based model for such strategies involves significant development efforts and is also associated with high computational cost. This paper proposes a black-box framework for CRS process control based on artificial neural network and principal components analysis. To identify the nonlinear system behavior of diesel combustion, a multi-input multi-output empirical model has been developed. The cylinder pressure trace is transformed into principal components coefficients space, and the neural network is used to predict the coefficients from operation parameters of diesel combustion. The in-cylinder pressure trace is then reconstructed by the predicted coefficients and pre-extracted principal components. The model has been evaluated with specific combustion features of CRS diesel engine experiments. The results show that the model successfully captured the combustion characteristics of CRS based diesel combustion processes with sufficient generalization ability.

Keywords: Fault detection & diagnostic, fault tolerant control, Detection, estimation
Abstract: Singular spectrum analysis (SSA) has become a popular and widely used forecasting and pre-processing technique in time series analysis which is currently exploited in chemical process monitoring and fault detection. Given its increased application and superior performance in comparison to conventional multivariate methods such as Principal Component Analysis (PCA) and Wavelets and its nonlinear extensions, it is relevant to study the variants of SSA and its applications in process monitoring. In this study SSA is combined with Kernel Multidimensional Scaling called Kernel Dissimilarity Scale Based Singular Spectrum Analysis (KDSSA) and is used to detect the faults in the Tennessee Eastman Process (TEP). The methodology is focused on three particular faults which were not observable with conventional multivariate methods and its nonlinear extensions. The monitoring results showed that the proposed method is efficient in detecting those faults in reduced number of modes. A unified monitoring index combined T^2 statistics with Q statistics is used to simplify the fault detection task.

Keywords: Adaptive control design, Distributed parameter systems, Stability analysis
Abstract: We present a generalization of the scalar Newton-based extremum seeking algorithm, which maximizes the map's higher derivatives in the presence of dynamics described by Reaction-Advection-Diffusion (RAD) equations. Basically, the effects of the Partial Differential Equations (PDEs) in the additive dither signals are canceled out using the trajectory generation paradigm. Moreover, the inclusion of a boundary control for the RAD process stabilizes the closed-loop feedback system. By properly demodulating the map output corresponding to the manner in which it is perturbed, the extremum seeking algorithm maximizes the n-th derivative only through measurements of the own map. The Newton-based extremum seeking approach removes the dependence of the convergence rate on the unknown Hessian of the higher derivative, an effort to improve performance and remove limitations of standard gradient-based extremum seeking. In particular, our RAD compensator employs the same perturbation-based (averaging-based) estimate for the Hessian's inverse of the function to be maximized provided by a differential Riccati equation applied in the previous publications free of PDEs. We prove local stability of the algorithm, maximization of the map sensitivity and convergence to a small neighborhood of the desired (unknown) extremum by means of backstepping transformation, Lyapunov functional and the theory of averaging in infinite dimensions.

Keywords: Adaptive control design, Optimal control design, Adaptive observers and estimators
Abstract: Abstract of not more than 250 words. In this paper, adaptive output feedback based tow-degree-of-freedom control with an adaptive output predictive control as a feedforward input is proposed for linear continuous-time systems. The method can design a stable and simple output predictive control based adaptive controller with higher control performance for uncertain systems. A simple adaptive output estimator and predictor for uncertain systems will be proposed to design a robust predictive controller for continuous-time systems, and the stability of the obtained control system will be maintained by ASPR based adaptive output feedback. The effectiveness of the proposed method is confirmed through numerical simulations for simple second order uncertain system.

Keywords: Mining, mineral and metal, Nonlinear system identification, Adaptive control design
Abstract: Meniscus velocity in continuous casting process is critical in determining the quality of the steel. Due to the complex nature of the various interacting phenomena in the process, designing model-based controllers can prove to be a challenge. In this paper a NARX neural network model is trained to describe the complex relationship between the applied magnetic field from an Electromagnetic Brake (EMBr) and the meniscus velocity. The data for the model is obtained using a laboratory scale continuous casting plant. The next step was to use Adaptive Model Predictive Control (MPC) to deal with the non-linearity of the model by adapting the prediction model to the different operating conditions. The controller will utilize the EMBr as an actuator to keep the meniscus velocity within the optimum range, and reject disturbances that occur during the casting process such as changing the casting speed.

Keywords: Performance and robustness analysis, Process control, Adaptive control design
Abstract: In industrial processes, it is necessary to maintain the user-specified control performance in order to achieve desired productivity. Many process control systems have the stochastic noise. For the noisy systems, the ordinary performance assessment method which based on the control error variance requires the long data windows, because the short data windows make the performance index oscillatory. The control performance deterioration can not be detected quickly by the long data windows. Moreover, the optimizations of FRIT for the steady state is difficult for the noisy systems, because of the high frequency component of the control error signal. In this paper, a performance monitoring method and a data driven PID parameter tuning method for the noisy systems are considered. Each approach effectively uses a low-pass filter. The effectiveness of the proposed schemes are verified by using a simulation example.

Keywords: Robotics. Mechatronics, Neuro-fuzzy modelling and control, Adaptive control design
Abstract: In this paper we propose a novel control architecture that employs an adaptive neural network (NN) for feed-forward compensation and a sectorial fuzzy controller in the feedback loop applied to the tracking motion control of robot manipulators. Both simulation and experimental results are presented in comparison with the original classic Proportional-Differential (PD) plus feed-forward controller, from which this new proposal is based, and two preliminary versions of the application of feed-forward sectorial fuzzy control and feed-forward adaptive neural nonlinear PD control to the tracking motion control of a two-degree of freedom (2-DOF) robot manipulator. The proposed controller has, in general, better performance than its counterparts in terms of transient response and steady-state error while it maintains one of the main characteristics of fuzzy controllers: Its tolerance to parameter deviation.

Keywords: Stochastic adaptive control design, Optimal control design, Adaptive control design
Abstract: The paper proposes the preference-elicitation support within the framework of fully probabilistic design (FPD) of decision strategies. Agent employing FPD uses probability densities to model the closed-loop behaviour, i.e. a collection of all observed, opted and considered random variables. Opted actions are generated by a randomised strategy. The optimal decision strategy minimises Kullback-Leibler divergence of the closed-loop model to its ideal counterpart describing the agent's preferences. Thus, selecting the ideal closed-loop model comprises preference elicitation.

The paper provides a general choice of the best ideal closed-loop model reflecting agent's preferences. The foreseen application potential of such a preference elicitation is high as FPD is a non-trivial dense extension of Bayesian decision making that dominates prescriptive decision theories.

The general solution is illustrated on the regulation task with a linear Gaussian model describing the agent's environment.

Keywords: Adaptive and optimal parameter estimators, Adaptive observers and estimators, Identification methods design and analysis
Abstract: We consider the problem of estimation of a (linearly) time-varying frequency of a sinusoidal signal with unknown phase and magnitude. Such a problem may arise in control design for optical telescopes that makes it interesting from the practical point of view. The existing methods typically use unbounded functions of time that, being multiplying by the input signal, may yield significant noise amplification and poor estimation performance. In contrast, we present a novel approach to the estimation of the linearly varying frequency based on iterative filtering yielding simple linear regression model with a scalar parameter. Illustrative numerical simulations support the theoretical results. We also present a comparison with other known methods.

Keywords: Adaptive observers and estimators
Abstract: Adaptive observers are recursive algorithms for joint estimation of both state variables and unknown parameters. Usually some persistent excitation (PE) condition is required for the convergence of adaptive observers. However, in practice, it may happen that the PE condition is not satisfied, because the available sensor signals do not contain sufficient information for the considered recursive estimation problem, which is ill-posed. To remedy the lack of PE condition, inspired by typical methods for solving ill-posed inverse problems, this paper proposes a regularized adaptive observer for general linear time varying (LTV) systems. Two regularization terms are introduced in both state and parameter estimation recursions, in order to preserve the state-parameter decoupling transformation involved in the design of the adaptive observer. Like in typical ill-posed inverse problems, regularization implies an estimation bias, which can be reduced by using prior knowledge about the unknown parameters.

Keywords: Adaptive observers and estimators, Nonlinear systems, Power & energy systems
Abstract: The problem of state and parameter estimation in photovoltaic (PV) systems is addressed. The maximum power point tracking (MPPT) techniques and controllers design involve the PV generator (PVG) delivered voltage and current. However, in situations where PV arrays are located in a remote site from the control unit of the converter, so as to profit from good solar radiation, PVG voltage and current measurements become difficult. From other side, the use of long PV cable between the PVG and the converter would produce substantial voltage drops in the cable, which would consequently result in MPPT control inaccuracies if only voltage and current sensed in the converter input side of the cable are used instead. To avoid this problem, an adaptive Kalman--like observer for PV systems is designed, in this paper. Using only voltage and current measurements in the converter input, the observer performs online estimation of the PVG output voltage and current as well as of the cable resistance and inductance, regardless of these parameters uncertainties. The convergence of the system state and parameters is shown by simulation.

Keywords: Linear systems, Adaptive and optimal parameter estimators, Hybrid systems
Abstract: A new DREM-based (Dynamic Regressor Extension and Mixing) modification for output adaptive controller with input multi-harmonic disturbance cancellation is proposed in this paper. This approach provides monotonic convergence of the disturbance internal model parameters' estimates to its true values. We also introduce a novel algorithm for the DREM-based estimator gains tuning in order to improve convergence under poor excitation. Parallel kinematics Ball-and-Plate robotic system is considered as a test-bed, while the non-prehensile ball stabilization in a predefined coordinates under bounded disturbances is a task to be solved.

Keywords: Statistical signal modelling and analysis, Detection, estimation, Non-Gaussian signals and noise
Abstract: Modern implementations of the Prony method have been used in the statistical analysis of sinusoidal and/or exponential signals distorted with noise. Modern implementations are autoregressive, using a series of matrix calculations and least-squares to calculate the values of interest from a signal; the frequency, decay constant, initial amplitude, and phase. In cavity ring-down spectroscopy, the frequency and decay constant of an exponentially decaying sinusoidal signal need to be obtained, in order to identify molecules and the chirality of these molecules, which may be applied in, for instance, development of pharmaceuticals. This method is applicable to signals from other fields - signals which are sinusoidal or exponential in nature. An implementation of the Prony method for cavity ring-down spectroscopy has been developed and characterised in Python.

Keywords: State observer & estimator design, Nonlinear control design
Abstract: One of the most widely studied dynamical systems in nonlinear control theory is the levitated ball. Several full-state feedback controllers that ensure asymptotic regulation of the ball position have been reported in the literature. However, to the best of our knowledge, the design of a stabilizing law measuring only the current and the voltage---so-called sensorless control---is conspicuous by its absence. Besides its unquestionable theoretical interest, the trade off between cost and reliability of position sensors for magnetic levitated systems, makes the problem of great practical application. Our main contribution is to provide the first solution to this problem without linearisation and signal injection. Instrumental for the development of the theory is the use of parameter estimation-based observers, which combined with the dynamic regressor extension and mixing parameter estimation technique, allow the reconstruction of the magnetic flux. With the knowledge of the latter it is shown that the mechanical coordinates can be estimated with suitably tailored nonlinear observers. Replacing the observed states, in a certainty equivalent manner, with a full information asymptotically stabilising law completes the sensorless controller design. Simulation results are used to illustrate the performance of the proposed scheme.