Keywords: System and Uncertainty Modeling, Computational Methods, Mechatronic Systems
Abstract: The scanning tunneling microscope (STM), a Nobel Prize-winning invention, has revolutionized surface science with its ability to image and manipulate matter at the atomic scale. While STM has traditionally been used for topographic imaging and spectroscopy, recent advances have expanded its applications to include atomically precise lithography, crucial for the development of future quantum electronic devices. Despite these advancements, the fundamental feedback control loop that governs STM operation has remained largely unchanged for the past 40 years. This presentation delves into the intricate interplay between STM feedback control and surface physics, exploring how innovative modifications to the control system can unlock new modes of imaging, spectroscopy, and lithography. Reimagining the STM’s control system is the key to pushing the boundaries of STM capabilities and opening new frontiers in nanoscale science and engineering.

Keywords: Autonomous Systems, H-infinity Control
Abstract: This paper presents a method for improving the performance level of the robust Hinf controllers. The improvement is achieved in an additive form, which contains a learning-based agent. The contribution of the presented method is that the design methods of the Hinf controller and of the learning-based agent are formed in a joint optimization. This results in the iterative design of the controllers within a reinforcement learning algorithm. The developed design method is applied to an autonomous vehicle control problem for lap time minimization. The presented simulation-based analysis shows that the proposed method can provide improved performance level, compared to the conventional Hinf control without extension or to Hinf control with extension but without joint optimization.

Keywords: Autonomous Systems, H-infinity Control, Nonlinear Control
Abstract: This paper aims to apply two classical and well-established controller architectures for re-entry to an innovative and realistic problem, as it is the re-entry of a flexible fairing and compare the achieved performances in a preliminary and simplified set-up. The considered platform is a 20 m fairing half, equipped with dedicated thrusters, intended as a recurring solution for recovery as part of the REFAIR project funded by ESA. The considered control solutions are a 𝐻∞ controller, with known stability and performance robustness, and a phase-plane controller, associated with simplicity and effectiveness. The control solution design is presented, and the results are compared, namely in terms of position dispersions at Mach 0.7 and fuel consumption. The suitability of the solutions is discussed by comparing the model agnostic approach of the phase plane controller with the model-based approach of the 𝐻∞ controller

Keywords: H-infinity Control, Vehicle Monitoring, Diagnosis and Control, Autonomous Systems
Abstract: In this work, we propose and experimentally validate a novel H∞ scheme for direct yaw moment control of modern vehicles. In particular, the proposed scheme seeks to enhance the robustness of a real (state-of-practice) PIDs. To this end, we tune the robust controller using the so-called “bicycle model”, accounting for a Linear Parameter Varying (LPV) reference model with consistent weights w.r.t. vehicle handling performance objectives. Accordingly, we present high-fidelity numerical validation results, along with real experimental vehicle tests under critical driving conditions in realistic city and mountain track circuits. Our findings confirm that the proposed LPV/H_∞ scheme indeed improves overall vehicle handling and driving stability.

Keywords: H-infinity Control, Robust Stability and Performance, Mu Analysis and Synthesis
Abstract: Among several challenges, wind resilience is one of the most desired features when designing a launch vehicle, as it allows higher structural flexibility and, thus, lighter vehicles. This paper addresses the problem of load relief and on-board wind anticipation in the context of a launch system through the design of a Wind Disturbance Observer (WDO) based on H_∞ robust synthesis for a flexible vehicle. First, a state-of-practice robust controller is designed to stabilize the flexible closed loop. Afterwards, the WDO design is described and the closed loop analyzed in terms of stability and robustness. Finally, the controller together with the WDO are tested in a high-fidelity nonlinear simulator, where a reduction in the load experienced by the vehicle is apparent, as desired.

Keywords: Data-driven Control, Model Predictive Control, Robust Stability and Performance
Abstract: This paper presents a data-driven receding horizon control framework for discrete-time linear systems that guarantees robust performance in the presence of bounded disturbances. Unlike the majority of existing data-driven predictive control methods, which rely on Willem’s fundamental lemma, the proposed method enforces set-membership constraints for data-driven control and utilizes execution data to iteratively refine a set of compatible systems online. Numerical results demonstrate that the proposed receding horizon framework achieves better contractivity for the unknown system compared with regular data-driven control approaches.

Keywords: Robust Stability and Performance, LMI and Convex Optimization, Structured and Unstructured Uncertainties
Abstract: This article deals with state feedback control of uncertain ostensible Metzler systems based on their hidden positive models. To address this problem, an approach is used to formulate stability conditions and parametric boundaries by introducing a decomposition of the ostensible Metzler matrix such that the resulting hidden part in the closed loop is positive and asymptotically stable. The design conditions are provided in terms of linear matrix inequalities with diagonal positive definite matrix variables to comply with the diagonal stabilizability rule. Finally, a numerical example is presented to confirm the validity of the analysis result.

Keywords: Robust Stability and Performance, Networked Control Systems, LMI and Convex Optimization
Abstract: Networked control systems (NCSs) play an important role in Industry 4.0 and the Internet of Things (IoT), offering benefits such as operational cost reduction, energy efficiency, and architectural flexibility. However, communication constraints, including limited bandwidth and delays, present challenges to closed-loop stability and performance. Event-triggered control (ETC) has emerged as a solution to optimize network usage while ensuring stability. This work focuses on the co-design of periodic event-triggered robust controllers for linear parameter-varying (LPV) systems to ensure the stabilization of the closed-loop system. Utilizing parameter-dependent looped-functionals, second-order polynomial negativeness, and Pólya’s theorem, LMI-based stability conditions are developed under a static event-triggered mechanism (ETM) structure. A differential evolution algorithm is introduced to reduce control signal updates compared to convex optimization procedures. Numerical validation demonstrates the effectiveness of the proposed approach, highlighting its advantages over existing methods.

Keywords: Robust Stability and Performance, Structured and Unstructured Uncertainties, System and Uncertainty Modeling
Abstract: Common worst-case analyses for uncertain finite-horizon systems consider quadratic performance metrics based on the strict Bounded Real Lemma. Thus, they assess system performance for bounded inputs, e.g., signals in L2, which exhibit a worst-case shape. Consequently, known disturbance characteristics are left unexploited and uncovered, leading to unnecessarily conservative results. The present paper develops a worst-case analysis covering arbitrarily L2-bounded worst-case signals and partially known disturbances simultaneously. This is achieved by modeling the latter using signal integral-quadratic constraints (IQCs). The resulting analysis condition relies on a dissipation inequality within the IQC framework for finite time horizon problems. This framework also readily allows to incorporate additional system uncertainties in the analysis. The approach's feasibility is demonstrated with the worst-case performance analysis of a small unmanned aerial vehicle in an urban environment.

Keywords: Robust Stability and Performance, Optimization Methods, Aerospace
Abstract: The H2 norm is a fundamental design metric in many control applications and it is therefore important to evaluate how it is affected by uncertainties in the model. In the space domain, the H2 norm is particularly significant when the Pointing Error Source (PES) of a satellite can be approximated by a white noise, which is often the case for microvibrations and acoustic disturbances. The present paper discusses a new method to identify a set of real parametric uncertainties which maximizes (resp. minimizes) the finite-frequency H2 norm of an uncertain Multiple-Input Multiple-Output (MIMO) linear system. To do so, the analytical expression of the finite-frequency H2 norm is first approximated as a sum of contributions on a discrete frequency grid. A constrained nonlinear optimization is then performed to maximize (resp. minimize) the so-obtained function. The proposed worst-case finite-frequency H2-norm analysis paves the way to a wide range of possible applications, specially when integrated into the Verification and Validation (V&V) process of space missions requiring high pointing performances. The theoretical results derived in the paper are implemented and successfully tested on models of increasing complexity.

Keywords: Hinf Control, Diagnosis and Control, Aerospace Dynamics
Abstract: This paper describes the newly included features in the LPVTools software suite and their application to the design of a flexible spacecraft attitude controller in the linear fractional transformation (LFT) framework. LPVTools is a Matlab Toolbox for modelling, analysis and controller synthesis for linear parameter-varying systems. It was originally developed by MUSYN Inc. and covers both LFT and gridded (Jacobian linearization) types of LPV system. The original version of LPVTools focused heavily on the latter. This paper presents newly added functionalities of the toolbox, which focus on the LFT framework.

Keywords: Hinf Control, Nonlinear Systems, Systems with Time-Delay
Abstract: Input-delayed, discrete-time Lifshitz-type nonlinear systems with stochastic uncertainties in their state-space model are considered. The problem of H_infty measurement-feedback control is solved, for the stationary case, via the application of predictor-type control. Following the solution for the nominal case, a robust solution is obtained for uncertain polytopic-type systems. The multiplicative noise appears in the system dynamic matrix, while the delay resided in the input to the system. In this problem, a cost function is defined which is the expected value of the standard H_infty performance index with respect to the uncertain parameters. An example is given that demonstrates the applicability of the theory.

Keywords: Other Applications of LPV Systems
Abstract: This paper presents the modeling, control design, and experimental validation of water level tracking in a three-tank system. Due to the system’s wide operating range, traditional linear controllers are insufficient to ensure consistent performance across all conditions. To address this limitation, LPV control theory is employed to design a controller that remains effective across a broad operating range. The nonlinear system is reformulated as a quasi-Linear Parameter Varying (quasi-LPV) model, enabling the design of a scheduled dynamic output feedback (DOF) controller. The design is carried out using a Linear Matrix Inequalities (LMI) based approach, leveraging the H_{infty} mixed sensitivity method to ensure robust stability and optimize performance metrics such as reference tracking and disturbance rejection. To assess the practical effectiveness of the proposed control strategy, real-time experiments are conducted on an actual three-tank setup. The results validate the controller’s capability to maintain stable operation, achieve accurate steady-state tracking, and effectively reject external disturbances, demonstrating its suitability for nonlinear process control applications.

Keywords: Uncertain Systems - LPVS, Hinf Control, Aerospace Dynamics
Abstract: Modern engineering problems often have complicated uncertain dynamics that are difficult to accurately model; but data describing these effects can be measured. This paper proposes a data-driven robust controller synthesis approach for linear parameter varying (LPV) systems. It uses an iterative synthesis approach separated into a nominal synthesis and robust performance analysis step. It uses quadratic constraints (QC) to re-formulate the induced L2-norm analysis step with data driven linear matrix inequalities (LMI). The approach is applied to the controller synthesis for a satellite with nonlinear sloshing dynamics. The resulting controller demonstrates better attitude control performance than a nominal controller.

Keywords: Uncertain Systems - LPVS, Predictive Control, Optimal Control
Abstract: Data-driven control is getting the spotlight, promising to enable control design directly from raw data while avoiding what is arguably the most time-consuming phase of the control design pipeline, modeling. Comparing and contrasting existing approaches for data-driven predictive control with a focus on LPV systems, this talk will accompany the audience on a journey toward recent advances in the field, unveiling the role of modeling assumptions and key connections with system identification..

Keywords: Aerospace, H-infinity Control
Abstract: This paper presents a systematic framework for applying H-infinity Loop Shaping to the design of Thrust Vector Control systems for the atmospheric ascent of rigid launch vehicles. H-infinity Loop Shaping offers a streamlined alternative to the widely used H-infinity Closed Loop Shaping by automatically ensuring robustness at the plant input and output and preventing the need to simultaneously tune multiple closed-loop transfer functions to achieve the desired goals. The proposed methodology simplifies controller synthesis while maintaining robust stability and performance, as demonstrated by stability margin, structured singular value, and worst-case gain analysis. Preliminary findings suggest equivalency between controllers designed using H-infinity Loop Shaping and H-infinity Closed Loop Shaping, with the former offering a more efficient and less complex approach. Future work will extend the guidelines to flexible launch vehicles and attempt to fully demonstrate the equivalence between controllers attained with both methods.

Keywords: Fault Detection and Isolation, H-infinity Control, Aerospace
Abstract: This article presents a fault-tolerant control (FTC) reconfiguration scheme designed to mitigate the impact of on-board failures in launch vehicles equipped with clustered rocket engines. The proposed recovery strategy makes use of a dynamic allocation function and replaces the nominal thrust vector control (TVC) controller with an FTC-based controller explicitly designed to be robust against a predefined failure scenario. Specifically, the FTC methodology is demonstrated for a 60% loss of thrust in a single engine. The FTC control design problem is formulated within the structured H-infinity control framework, incorporating the failure directly into the design process via modeling. Simulation results confirm that the FTC controller effectively achieves the desired control objectives, demonstrating its robustness and efficacy in handling engine failures.

Keywords: Vehicle Monitoring, Diagnosis and Control, Fault Detection and Isolation, Aerospace
Abstract: The probabilistic-adaptive Kalman filter (pAKF) algorithm is developed for fault-tolerant estimation of unmanned aerial vehicle (UAV) states in the face of measurement faults. The suggested pAKF is based on calculating the posterior probability of normal operation of the system for the present measurement. It is suggested that this probability be computed using the posterior probability density of the normalized innovation sequence at the current estimation step. As a result, the system corrects defects in the estimating system while preserving the estimation's good behavior. The developed pAKF algorithm is used for fault-tolerant UAV state estimation and tested under a variety of measurement failure scenarios, including continuous measurement bias, measurement noise increment, instantaneous abnormal measurements, and sensor zero-output signal.

Keywords: Aerospace, Optimal Control and dynamic optimization
Abstract: This paper addresses the control problem of circular take-off of tethered aircraft under varying wind conditions, which is a problem arising in Airborne Wind Energy Systems (AWES). The study focuses on a less-explored CTOL configuration using kites with landing gear and propellers. A multivariable controller is developed to manage altitude control under steady flight, addressing the challenges of variable wind conditions. The proposed control architecture is validated through simulations under both constant and varying wind speeds. The findings demonstrate the feasibility of the proposed control strategy and contribute towards the autonomy and robustness of AWES.

Keywords: H-infinity Control, Robust Stability and Performance, Aerospace
Abstract: Flight control system design for the Flying-V has been an active research area. However, despite the strengths of H-infinity control, this framework has not yet been considered for the system design. Therefore, this study details the synthesis of a longitudinal control law using the robust control signal-based H-infinity framework. The trimming procedure used to obtain operating points and linearized flight dynamics is explained, followed by a description of the design requirements which are systematically converted into hard constraints for synthesis. A structured controller design is conducted and the resulting system is evaluated in terms of performance and robustness in linear and nonlinear settings. Results indicate effective disturbance and noise rejection, stability under parametric uncertainties, Level 1 handling qualities predictions, and adequate performance. The C∗ control law effectiveness paves the way for future enhancements in gain- scheduled robust controllers for the Flying-V and for the extension to lateral-directional designs.

Keywords: LMI and Convex Optimization, Robust Stability and Performance, Process Control
Abstract: This paper presents a method for designing the robustness filter in the Simplified Filtered Smith Predictor control scheme in discrete time. The proposed design simultaneously considers process uncertainty and disturbance attenuation problems in the robustness filter synthesis. The novelty of the method consists of evaluating the robust stability condition by linear matrix inequalities to design the robustness filter parameters assuring the closed-loop stability in the presence of process model uncertainty and closed-loop regulation considering the process-specified disturbances. A numerical example considers first-order systems with time delay and illustrates the advantages of the proposed method.

Keywords: Model and Controller Reduction, LMI and Convex Optimization
Abstract: We present a generic algorithm for estimating quasi-Linear Parameter Varying (qLPV) models using radial basis function (RBF) from state and output measurements of discrete autonomous systems. The proposed method guarantees a bounded approximation error across the entire training dataset and incorporates global stability constraints on the null equilibrium point when known. Extensions to continuous-time systems and systems with external inputs further enhance its versatility. The approach is illustrated on FEM model of a soft pendulum, demonstrating its capability in capturing complex system dynamics. The algorithm reduces the number of vertices required in the polytopic representation, maintaining accuracy while minimizing computational complexity.

Keywords: Hybrid and Switched Systems, LMI and Convex Optimization, Computational Methods
Abstract: In this paper, we address the problem of designing an aperiodic sampled-data controller stabilizing the zero-input equilibrium of an uncertain affine plant. The closed-loop system is modeled as a hybrid dynamical system incorporating a timer triggering the occurrence of the sampling events and two memory states storing the value of the controller state and controller output at each sampling time. Necessary and sufficient conditions on the controller parameters are given to establish the sought property. A constructive controller design algorithm based on sum-of-squares programming is given. A numerical example illustrates the effectiveness of the approach.

Keywords: Optimal Control and dynamic optimization, LMI and Convex Optimization, Computational Methods
Abstract: This paper studies distributionally robust regret-optimal (DRRO) control with purified output feedback for linear systems subject to additive disturbances and measurement noise. These uncertainties (including the initial system state) are assumed to be stochastic and distributed according to an unknown joint probability distribution within a Wasserstein ambiguity set. We design affine controllers to minimise the worst-case expected regret over all distributions in this set. The expected regret is defined as the difference between an expected cost incurred by an affine causal controller and the expected cost incurred by the optimal noncausal controller with perfect knowledge of the disturbance trajectory at the outset. Leveraging the duality theory in distributionally robust optimisation, we derive strong duality results for worst-case expectation problems involving general quadratic objective functions, enabling exact reformulations of the DRRO control problem as semidefinite programs (SDPs). Focusing on one such reformulation, we eliminate certain decision variables. This technique also permits a further equivalent reformulation of the SDP as a distributed optimisation problem, with potential to enhance scalability.

Keywords: Constrained Control, Hybrid and Switched Systems, LMI and Convex Optimization
Abstract: This paper addresses the problem of local stability analysis of the connection between a continuous-time linear system with input saturation and a discrete-time output feedback controller updated aperiodically. To address the problem, we consider a hybrid system model to represent the closed-loop system dynamics. Using a quadratic timer-dependent Lyapunov function candidate and a generalized sector condition to deal with saturation effects, timer-dependent LMI conditions are formulated to certify the local stability of the origin and to provide estimates of its region of attraction. Considering a polynomial timer dependency, optimization problems based on semidefinite programming are proposed to maximize an estimate of the region of attraction of the origin or the upper bound of the possible variation of the sampling interval for which the stability is ensured, given a set of admissible initial conditions. A numerical example illustrates the application of the method and the conservatism reduction when compared to a previous approach.

Keywords: Optimal Control and dynamic optimization, Biological Systems, LMI and Convex Optimization
Abstract: This work is devoted to the discussion of a robust approach for counterfactual generation in a control framework. Counterfactual is a concept from the field of logic, which in last years has been adopted in the context of artificial intelligence to describe the minimum changes in the input variables required to vary the outcome of a classification algorithm. In general, this framework for counterfactuals shows some limitations inherently due to the fact the most of the machine learning models leverage black box approaches, overlooking the physics of the underlying system. In this work we discuss a control system approach to derive counterfactuals that are informed by the knowledge about the system dynamics, in the very general case of a system affected by model parameter uncertainties.

Keywords: Model Predictive Control, Energy Systems, Process Control
Abstract: This work proposes a cyber-resilient Distributed Model Predictive Control framework to improve microgrid security and operational reliability against cyber threats. It specifically addresses manipulation attacks on the weight negotiation process within the Alternating Direction Method of Multipliers (ADMM) algorithm, where a malicious agent can alter weight updates, resulting in a cyber-attack. To counter these threats, the proposed approach integrates anomaly detection mechanisms that analyze negotiation patterns and identify malicious behavior through residual analysis. Upon detecting deviations in critical operational parameters, this system implements targeted mitigation actions to minimize the attack's impact. Simulation results demonstrate the effectiveness of this approach in detecting and mitigating ADMM-based manipulation attacks, emphasizing the necessity of integrating cybersecurity mechanisms into distributed control frameworks for enhanced microgrid resilience.

Keywords: Virtual Reference Feedback Tuning, Aerospace Dynamics
Abstract: This paper presents a variable L0 guidance parameter-based path-following method for airborne wind energy systems. The parameter L0 utilizes an exponential function of the cross-track error to govern the converging behavior of the vehicle relative to the desired path. Simulation results are presented utilizing a kite kinematic model. The comparative studies are carried out with respect to the constant L0 based guidance law thus illustrating the efficacy of the proposed method. Results emphasize intelligent choice of L0 parameter for accurate path-following while satisfying design criteria.

Keywords: Identification, Energy Systems, Hybrid and Switched Systems
Abstract: Li-ion batteries are widely used in electric vehicles, grid storage, and portable electronics. Battery Management Systems play a crucial role in ensuring the safety, efficiency, and longevity of Li-ion batteries. Accurate battery modelling is essential for effective battery management functionality, enabling precise state of charge/ state of health estimation, as well as protection against hazardous conditions such as overcharging or overheating. This article explores system identification techniques for battery modelling using a piecewise LTI approach where separate LTI models are identified for different state of charge intervals. A modified Thévenin circuit is employed, where the open-circuit voltage is represented by a capacitor that models the bulk charge storage. The capacitance of this element is dependent on the state of charge, reflecting the nonlinear nature of the battery’s charge storage mechanism. Additionally, parallel resistor-capacitor networks capture transient voltage recovery dynamics. The identification process estimates the battery parameters from experimental data, and the resulting piecewise models are interpolated using cubic splines to construct a linear parameter-varying (LPV) representation of the system. The proposed methodology was validated through experimental results, demonstrating its effectiveness in enhancing battery management performance. Namely, (i) the model accurately captures the battery's voltage response with minimal error. (ii) the LPV model obtained by fitting splines to the estimated parameters demonstrates a level of accuracy comparable to that of the piecewise LTI model. (iii) the model robustness was validated through a continuous discharge test, showing strong agreement with experimental data and, therefore, demonstrating its reliability in real-world operating conditions. These results highlight the potential of the proposed methodology in improving battery management systems.

Keywords: Energy Systems, System and Uncertainty Modeling
Abstract: This paper describes the development of a Digital Twin (DT) model for a Proton Exchange Membrane (PEM) electrolyzer based on a phenomenological model. The DT model incorporates the electrochemical and thermal aspects of the electrolyzer, driven by the energy balance of the PEM electrolyzer. The model has been validated with experimental data from a laboratory-scale electrolyzer, but can be adapted to other PEM electrolyzers through parameter adjustment, enabling the DT to act as a dynamic and adaptive asset. In this paper, we highlight the application of the DT model in the field of renewable energy. We discuss the advantages and disadvantages of the DT model, which is a key technology to exploit the data generated in the industry, which can be used for better decision-making supported by AI, modeling and simulation.

Keywords: Model Predictive Control, Constrained Control, Optimization Methods
Abstract: This paper presents a model predictive control (MPC) with constraints for temperature control of Proton Exchange Membrane (PEM) electrolyser. The strategy is based on an MPC derived from a state-space representation that includes a disturbance model. Constraints are handled using a geometric approach known as the constraint mapping law, avoiding the need for a quadratic programming (QP) optimizer. The proposed controller offers two additional degrees of freedom in the control strategy: one for tuning the disturbance model and another for adjusting the cost function by adding a slack variable to the output constraint. Simulations and a comparative analysis highlight the advantages of the proposed controller, considering both its performance in the time domain and its computational efficiency.

Keywords: Data-driven Control, Energy Systems, Nonlinear Control
Abstract: In this paper we study a deep learning-based method to enhance the estimation accuracy of a nonlinear observer with partially unknown output functions. This technique is particularly useful for the problem of State of Charge estimation in vanadium flow batteries. The key innovation of this approach is the direct reliance on terminal voltage measurement and the incorporation of a machine learning algorithm to learn the battery’s overpotentials. The overpotentials are represented by a neural network trained on data produced by a conventional observer, which determines species concentration using a physical electrochemical model and open-circuit voltage measurements. Once trained, this model is integrated into the observer to enhance State of Charge estimation precision. The stability of the deep learning-based observer is formally proved. Additionally, the method is validated through experimental evaluations on a real vanadium flow battery system.

Keywords: H-infinity and Optimal Estimation
Abstract: This paper introduces an interval observer design with state lifting for discrete-time (DT) and continuous-time (CT) linear systems under additive bounded uncertainties. Our approaches circumvent the need for time-varying or time-invariant coordinate transformations by introducing two state lifting methods based on the Cayley-Hamilton theorem and a matrix exponential property. Further, it is demonstrated that the interval observers for the lifted system are at least as good as interval observers for the original non-lifted system with minimal increase in computational complexity, while also being applicable (feasible) to a broader range of systems due to the flexibility of increased degrees of freedom in the lifted observer. Finally, we demonstrate and discuss the effectiveness of the proposed approach on a wide range of CT and DT examples, including as a viable replacement for coordinate transformations.

Keywords: H-infinity and Optimal Estimation, LMI and Convex Optimization, Mechatronic Systems
Abstract: Vehicle suspensions are complex systems when they can modify the damping forces according to a control approach. This complexity is even more higher when all system variables are not available and the operating conditions are time-varying. To address this problematic, this paper proposes a robust full-order observer design for the damper forces in a full-vehicle suspension system considering the nonlinear dynamics of four Magneto-Rheological (MR) dampers as semi-active actuators. The proposed robust observer design is based on the direct Lyapunov method through LMI-based conditions to guarantee robustness mainly to road disturbances, dynamic actuation signals, and measurement noise. The above robustness capabilities were evaluated using three different simulation scenarios in a MATLAB/Simulink environment. Simulation results showed that the observation error trends to zero in a fast and stable way for the three tests, demonstrating the robustness performance of the proposed observer in face to different road roughness, dynamic changes in the actuation signals of the MR dampers and measurement noise at different levels.

Keywords: Identification
Abstract: This paper studies linear parameter-varying (LPV) stochastic systems to explore noise models for system identification. It is known that, in the conventional LPV stochastic systems, where system matrices and noise covariances statically depend on the present parameter, the Kalman gain and innovation covariance in the finite-interval innovation representation dynamically depend on parameters. Using the output covariance, this paper demonstrates that, in the finite-interval innovations representation of the LPV stochastic system whose input and direct transmission matrices are functions of parameters from the infinite past, the Kalman gain and innovation covariance also dynamically depend on parameters from the infinite past.

Keywords: Identification, Optimization Methods, Manufacturing Processes
Abstract: Some industrial processes require closed-loop system identification due to constraints on direct system access, leading to challenges with cross-correlated signals. Instrumental variables can estimate noise-free control and output signals. An optimal filter minimizes noise while preserving essential signal information. In Computer Numerical Control (CNC) machining, the spindle speed control loop involves a parallel proportional-integral controller with specific prefiltering for the integral component, and consequently the classic CLSRIVC method does not work properly, even if the output is affected by white noise. This paper investigates various closed-loop identification methods under white noise conditions and evaluates their statistical properties using Monte Carlo simulations.

Keywords: Robust Stability and Performance, System and Uncertainty Modeling, H-infinity and Optimal Estimation
Abstract: This paper proposes convex conditions for the observer design of nonlinear continuous-time systems. A broad class of nonlinear systems can be tackled by the proposed technique. A spatial discretization is employed, and an approximate model is obtained within the error matrices that measure the difference between the nonlinear system and the approximated one. The conditions are formulated as parameter-dependent matrix inequalities and ensure that the observer can asymptotically follow the states of the original nonlinear system while guaranteeing a bound to the mathcal{L}_2-gain from the disturbance input to the estimation error. Numerical experiments are used to illustrate the features of the proposed method.

Keywords: Nonlinear Systems, Stability and Stabilization, Optimal Control
Abstract: The objective of this paper is to present an efficient methodology for synthesizing control systems for nonlinear systems subjected to bounded external disturbances. Nonlinear systems can be embedded onto LPV systems (quasi-LPV formalism) but said embedding depends on the modelling region; modelling region depends on which positively invariant sets can be proved, thus an iterative LMI approach ensues, to be explored in this work. A gain-scheduled control approach is proposed, where the control parameters are designed using iterative Linear Matrix Inequalities (LMIs) to approximate the smallest possible invariant set containing the origin. Control design conditions are derived by applying the Lyapunov method in conjunction with the H_1 star norm, and appropriately defined multipliers. A numerical example is provided to demonstrate the proposed methodology.

Keywords: Uncertain Systems - LPVS, Stability and Stabilization, Nonlinear Systems
Abstract: This paper proposes a linear matrix inequality-based iterative approach for output-feedback stabilization of linear parameter-varying discrete-time systems subject to state, control magnitude, and control-rate symmetrical constraints. Using an augmented state-space description, an incremental control law that includes the actual output measurements is constructed in terms of parameter-dependent output-feedback gains. The stabilization conditions consider the control signal constraints and allow an estimate of the domain of attraction in terms of a contractive ellipsoidal-based set. Finsler's Lemma manipulations of the stability conditions yield matrix inequalities suitable for solving by an iterative algorithm that iterates directly on the controller parameter space. Simultaneously, the algorithm minimizes a bound to the decay rate of the system and computes an estimate of the domain of attraction as large as possible. Control design cases allowing or avoiding control-rate saturation are addressed and illustrated by numerical examples, including comparisons with a polyhedral set approach.

Keywords: Nonlinear Systems, Stability and Stabilization
Abstract: This paper presents three main contributions to the field of multi-step system identification. First, drawing inspiration from Neural Network (NN) training, it introduces a tool for solving identification problems by leveraging first-order optimization and Automatic Differentiation (AD). The proposed method exploits gradients with respect to the parameters to be identified and leverages Linear Parameter-Varying (LPV) sensitivity equations to model gradient evolution. Second, it demonstrates that the computational complexity of the proposed method is linear in both the multi-step horizon length and the parameter size, ensuring scalability for large identification problems. Third, it formally addresses the "exploding gradient" issue: via a stability analysis of the LPV equations, it derives conditions for a reliable and efficient optimization and identification process for dynamical systems. Simulation results indicate that the proposed method is both effective and efficient, making it a promising tool for future research and applications in nonlinear system identification and non-convex optimization.

Keywords: Nonlinear Systems, Robustness Issues
Abstract: Modeling non-linear systems has always been a challenge in the field of control engineering. Linear Parameter Varying (LPV) models can be a valid choice to model complex systems, since they have a simple linear structure, but time varying coefficients that captures the system dynamics according to a scheduling signal measured from the system. A common approach to identify a LPV system in an ARX form is the Least Squares Support Vector Machines (LS-SVM) method. However, due to its computational complexity, it is difficult to employ such algorithm in online applications, when a model must be identified each time a new datum is collected from the system. An efficient recursive update algorithm has been recently presented in the literature for such cases, where only the most informative data points are selected to update the model, thus generally reducing the required computational effort. However, in certain conditions such algorithm selects too many data points, still leading to an high computational time. In this work, a quadratic entropy based algorithm is proposed to overcome the limitations found in the literature, providing a better trade-off between identification accuracy and computational time.

Keywords: Nonlinear Systems
Abstract: In this paper, an automated linear parameter-varying (LPV) model conversion approach is proposed for nonlinear dynamical systems. The proposed method achieves global embedding of the original nonlinear behavior of the system by leveraging the second fundamental theorem of calculus to factorize matrix function expressions without any approximation. The implementation of the proposed method in the LPVcore toolbox for Matlab is discussed, and its performance is showcased on a comprehensive example of automated LPV model conversion of an unbalanced disk system, which is then used to design an LPV controller that is deployed on the original nonlinear system. In addition, the conversion capabilities are further showcased by LPV embedding of a three-degree-of-freedom control moment gyroscope. All software implementations are available at www.lpvcore.net.

Keywords: Predictive Control, Nonlinear Systems
Abstract: The Linear Parameter Varying (LPV) approach for Nonlinear Model Predictive Control (NMPC) has been extensively discussed in recent literature as a promising technique to reduce the overall computational time of typical NMPC schemes, while being able to maintain prediction accurateness and control performances. However, when it comes to practical engineering applications involving real-time systems operating under strict sampling periods, numerical burden challenges still persist. In this work, we develop and validate a novel library- independent embedded optimization based on the LPV MPC approach. In particular, we rely in the logarithmic barrier interior-point (LB-IP) method appropriately tuned as a dedicated solver for LPV MPC using C/C++ syntax. Our results comprise an experimental processor- in-the-loop (PIL) validation result for a drone landing problem using our solver. Finally, we discuss practical aspects of embedding LPV MPC algorithms and debate advances using the LPV approach for hardware-based experiments, without the need for any proprietary toolbox.