Parameter-varying Systems Research Articles

Generalized [formula omitted] observer for road profile estimation in the automotive suspension system

This study develops a generalized H2 observer to estimate the road profile in the semi-active automotive suspension system. The dynamics of the quarter-car model are represented in the descriptor nonlinear parameter-varying system framework, with the road profile as a system's state that is of arbitrary dynamics. Then, a road profile estimation method is designed by using a generalized H2 observer, which utilizes the onboard accelerometers as the observer's input. The adverse impact of measurement noises on the accuracy of estimation results is alleviated via the generalized H2 framework. The proposed observer is designed by solving an LMI-based constrained optimization problem. Frequency domain analysis and time domain simulations illustrate the efficiency of the proposed strategy

Gain-scheduled filter design with different time delays for T-S fuzzy systems

In this article, the authors study a problem of parameter-varying systems that gain-scheduled [Formula: see text] filtering T-S fuzzy problems by appearing of time-varying delays. Our paper also aims to establish filters that deal with communication delays. Traditional studies often study delay-free filters, but these filters have a more general form. In addition, a nonlinear fractional transformation structure has been incorporated into this filter, which allows its parameters to vary. The authors implement fuzzy Lyapunov–Krasovskii functionals used to intend the delayed fuzzy filters of this study, and delay-dependent circumstances are obtained for stability and performance analysis. The solution of the presented linear matrix inequalities (LMIs) provides the filter parameters. This method is finally justified with an example that illustrates its effectiveness.

TVIE-based fault-tolerant model predictive control for trajectory tracking of mobile robot

This paper investigates the trajectory tracking control issue for a linear parameter-varying (LPV) system of a wheeled mobile robot (WMR) with actuator fault and constraints, where a time-varying intermediate estimator (TVIE)-based fault-tolerant model predictive control (MPC) method is proposed. To obtain the real system with actuator fault, based on the existing traditional IE, an optimized objective function is designed to update its observer gain online, which results in a TVIE. A new estimation-based predictive model in MPC is designed by introducing the estimations of error state and fault from the TVIE. Moreover, compared with the existing IE or extended state observer (ESO), the estimation performance of TVIE is better. Then the MPC optimization strategy is used to design fault-tolerant controllers. To guarantee stability and recursive feasibility, the bimodal MPC strategy is used, where a terminal penalty and a terminal constraint are included. Finally, the effectiveness and superiority of the proposed approach is illustrated in experiment.

Risk-Informed Model-Free Safe Control of Linear Parameter-Varying Systems

Risk-Informed Model-Free Safe Control of Linear Parameter-Varying Systems

Certificates of nonexistence for analyzing stability, stabilizability and detectability of LPV systems

By computing Lyapunov functions of a certain, convenient structure, Lyapunov-based methods guarantee stability properties of the system or, when performing synthesis, of the relevant closed-loop or error dynamics. In doing so, they provide conclusive affirmative answers to many analysis and design questions in systems and control. When these methods fail to produce a feasible solution, however, they often remain inconclusive due to (a) the method being conservative or (b) the fact that there may be multiple causes for infeasibility, such as ill-conditioning, solver tolerances or true infeasibility. To overcome this, we develop linear-matrix-inequality-based theorems of alternatives based upon which we can guarantee, by computing a so-called certificate of nonexistence, that no poly-quadratic Lyapunov function exists for a given linear parameter-varying system. We extend these ideas to also certify the nonexistence of controllers and observers for which the corresponding closed-loop/error dynamics admit a poly-quadratic Lyapunov function. Finally, we illustrate our results in some numerical case studies.

Disturbance Compensator Design Based on Dilated LMI for Linear Parameter-Varying Systems

Disturbance Compensator Design Based on Dilated LMI for Linear Parameter-Varying Systems

Parameter-dependent conditions for H ∞ stabilisation of polynomial parameter-varying system with delay

This paper considers the problems of achieving exponential stability and H ∞ stabilisation for polynomial parameter-varying system with time-varying delay. Unlike some existing linear parameter-varying results that treat system parameters as time invariant factors, this paper makes full use of the nonlinearity and time-varying characteristics of system through introducing a novel delay-and-parameter-dependent Lyapunov function. The main conclusions are discussed in three cases (system without input, system with disturbance input, system with disturbance input and control input). And the H ∞ stabilisation problem is solved by constructing a controller which is inserted with system parameters and their derivatives. The structures of Lyapunov function and controller lead to that the derived criteria for exponential stabilisation are expressed by state-and-parameter-dependent linear matrix inequalities, which are efficiently solved by sum-of-squares program. The effectiveness and superiority are verified through two numerical examples.

Event-triggered dynamic output-feedback control for LPV systems

This paper addresses the co-design of event-triggered dynamic output-feedback (DOF) control for discrete-time linear parameter-varying (LPV) systems. Two independent event-triggering schemes are introduced to determine when to transmit data from the sensor to the controller and from the controller to the actuator channels. Enhanced conditions employing linear matrix inequalities (LMIs) are derived to establish constructive criteria for simultaneously designing the gain-scheduled DOF controller and the triggering mechanisms, ensuring the asymptotic stability of the closed-loop LPV system's origin. Additionally, a convex optimisation problem is proposed to enlarge the inter-event sampling on the independent channels of sensor-to-controller and controller-to-actuator. Numerical examples are provided to illustrate the effectiveness of the proposed method.

Fault estimation for a class of nonlinear algebro-differential parameter-varying systems

This paper presents a methodology to simultaneous estimate state variables and actuator fault for descriptor nonlinear parameter-varying systems. This class of systems is composed of an interpolated parameter-varying linear part and Lipschitz nonlinear one. The proposed observer structure allows some robustness and steady state accuracy in face to parametric uncertainties. The conditions of existence and stability are given in terms of LMIs (Linear Matrix Inequalities). The obtained results are illustrated on the heat exchanger system with two countercurrent cells model with actuator fault.

Robust Adaptive Control of Linear Parameter-Varying Systems with Unmatched Uncertainties

In control of aerospace systems with large operating envelopes, it is often necessary to adjust the desired dynamics according to operating conditions. This paper presents a robust adaptive control architecture for linear parameter-varying (LPV) systems that allows for the desired dynamics to be systematically scheduled, while being able to handle a broad class of uncertainties, both matched and unmatched, which can depend on both time and states. The proposed controller adopts an L1 adaptive control architecture for designing the adaptive control law and peak-to-peak gain (PPG) minimization for designing the robust control law to mitigate the effect of unmatched uncertainties. Leveraging the PPG bound of a LPV system, we derive transient and steady-state performance bounds in terms of the input and output signals of the actual closed-loop system with respect to a nominal system. The proposed control architecture is applied to control the longitudinal motion of an F-16 aircraft operating within a large envelope. Simulation results using both LPV and fully nonlinear models validate the efficacy of the proposed method.

Asynchronous model predictive control of LPV systems with stochastic communication protocol

This study is dedicated to exploring the challenge of asynchronous resilient robust model predictive control (RMPC) for linear parameter-varying (LPV) systems operating under a stochastic communication protocol (SCP). In contrast to the conventional Markov-based SCP, a novel sojourn probability-based SCP is introduced to regulate packet transmissions. This innovative approach simplifies the determination of transition probabilities and lessens the computational burden. Acknowledging the challenges associated with observing sojourn probability information, a mode detector is employed to describe the connection between mode discrepancies. To address parameter uncertainties, a novel detected-mode-based resilient control law is formulated to ensure the mean-square stability of the LPV system within the resilient RMPC framework. Additionally, an online algorithm for resilient RMPC is presented, grounded in an auxiliary optimization problem. Ultimately, the effectiveness of the proposed control strategy is validated via a high-purity distillation process model.

[formula omitted] output tracking control for polynomial parameter-varying systems via homogeneous Lyapunov methods

This paper investigates the H∞ output tracking control for polynomial parameter-varying systems—a class of nonlinear parameter-varying systems. Based on the homogeneous polynomial Lyapunov function (HPLF), a state feedback controller is presented to make the augmented system (composed of the original system and the tracking error system) robust exponentially stable, so that the output of the original system can track the reference signal and satisfy the H∞ output tracking performance. The conservativeness of the theoretical results is reduced due to the following facts: (1) the HPLF can depend on the full states and time-varying parameters; and (2) there are no constraints on the input coefficient matrix and the inverse of the Lyapunov matrix. In particular, when the system states and time-varying parameters are confined to a compact set, local results are obtained based on the generalized S-procedure. The solvable conditions are given in terms of state-and-parameter-dependent linear matrix inequalities, which can be solved by sum of squares (SOS) techniques. Finally, the feasibility and effectiveness of the proposed method are verified by a numerical example and the heading control of unmanned surface vehicle.

Controlling neural activity: LPV modelling of optogenetically actuated Wilson–Cowan model * *This work was supported by ANPCyT, Ministry of Science & Technology, Argentina Grant PICT2017-2417. Demián García-Violini is supported by the Agencia I+D+i, Ministry of Science & Technology, Argentina, under PICT-2021-I-INVI-00190.

Objective. This paper aims to bridge the gap between neurophysiology and automatic control methodologies by redefining the Wilson–Cowan (WC) model as a control-oriented linear parameter-varying (LPV) system. A novel approach is presented that allows for the application of a control strategy to modulate and track neural activity. Approach. The WC model is redefined as a control-oriented LPV system in this study. The LPV modelling framework is leveraged to design an LPV controller, which is used to regulate and manipulate neural dynamics. Main results. Promising outcomes, in understanding and controlling neural processes through the synergistic combination of control-oriented modelling and estimation, are obtained in this study. An LPV controller demonstrates to be effective in regulating neural activity. Significance. The presented methodology effectively induces neural patterns, taking into account optogenetic actuation. The combination of control strategies with neurophysiology provides valuable insights into neural dynamics. The proposed approach opens up new possibilities for using control techniques to study and influence brain functions, which can have key implications in neuroscience and medicine. By means of a model-based controller which accounts for non-linearities, noise and uncertainty, neural signals can be induced on brain structures.

Integrated sensor FTC using integral sliding mode control

In this paper, a sliding mode sensor fault tolerant control scheme which involves a first order sliding mode observer, fault compensation logic and an integral sliding mode controller, is proposed for a class of uncertain linear parameter-varying systems. The proposed scheme has the capability to retain near nominal fault-free performance in the face of a class of sensor faults/failures. In particular, the closed-loop stability of the sensor fault tolerant scheme involving the sliding mode observer and the sliding mode controller in the presence of faults and uncertainty, is rigorously analysed. Furthermore, the paper proposes an algorithm to simultaneously synthesize the design freedom associated with the observer gains and control law despite the lack of a separation principle in the closed loop system overall caused by the uncertainty. The proposed scheme is validated using a commercial aircraft model. Good simulation results show the efficacy of the scheme.

A new approach for dynamic output feedback control design of time-delayed nonlinear systems

This paper introduces a full-order dynamic output-feedback (DOF) controller for discrete-time nonlinear systems with time-varying delays represented by Linear Parameter-Varying (LPV) systems. The controller design is carried out by developing delay-dependent Linear Matrix Inequality based conditions using Lyapunov–Krasovskii stability arguments. A notable characteristic of the proposed approach is that the dynamic controller gains are directly obtained, without the need for variable transformations, equality constraints, or iterative algorithms. This feature sets it apart from many existing approaches in the literature and simplifies the design process. Furthermore, the proposed approach guarantees the local asymptotic stability of the origin of the closed-loop system and provides an estimated admissible initial condition region. The correct operation of the system is ensured once the state trajectories initiated within the admissible initial condition region remain enclosed in the validity domain of the LPV model. Numerical examples are provided to illustrate the potential and effectiveness of the proposed conditions.

Finite-time bumpless transfer control problem for switched LPV systems with guaranteed switching frequency

For the switched linear parameter-varying (LPV) systems, the finite-time bumpless transfer control (FTBTC) issue is addressed by utilising the parameter-dependent multiple piecewise Lyapunov function method. First, for the switched LPV systems, a finite-time bumpless transfer performance is proposed, which only demands that bumpless transfer inequation holds in the activated interval in place of entire intervals. Second, a switching law depending on external parameters, system state, dwell time is designed to guarantee switching frequency. Third, a time-varying switching controller is designed, under which a solvable condition of the FTBTC issue is presented. It allows the FTBTC issue of each subsystem to be unsolvable. Finally, an aero-engine model is established to confirm the availability of the proposed scheme.

Orthotope-search-expansion-based extended zonotopic Kalman filter design for a discrete-time linear parameter-varying system with a dual-noise term

A novel algorithm utilizing an extended zonotopic Kalman filter based on the orthotope search expansion method is introduced to solve the state estimation problem in discrete-time linear parameter-varying systems when the dual noise of the systems is assumed to be bounded but unknown. First, to identify unknown parameters, an orthotope search expansion method is proposed with a measurement strip constraint. Subsequently, based on the parameter identification orthotopic set, an extended zonotopic Kalman filter algorithm is proposed to derive an estimation interval that wraps the true state of the system. Next, by minimizing the size of the zonotope, the optimal gain matrix for the extended zonotopic Kalman filter algorithm is determined. Finally, the proposed methods are demonstrated for their effectiveness and accuracy through the presentation of two simulation examples.

A new H∞ observer for continuous LPV systems with unknown inputs using an HOSM differentiator

Abstract The main contribution of this paper is the development of $H_{\infty }$ state and unknown input (UI) observers for noisy linear parameter-varying (LPV) systems. The observers are constructed in order to be unbiased (in particular the state estimation error is decoupled from the UI) and with a minimum $L_{2}$ transfer between the perturbations (that are assumed to be with finite energy) and the estimation errors. Contrary to equivalent observers developed in the literature, the present one relaxes a widely used rank condition on the system matrices for decoupling the UI. In order to do so, high-order derivation is needed, which is done using a high-order sliding modes differentiator. A method is given to design observer gains for LPV systems under polytopic form. Finally, three examples illustrate some aspects of the theoretical contributions, and compare this work to the existing ones.

[formula omitted] gain-scheduled dynamic output feedback control with transient performance applied to electrical microgrid

This paper introduces an approach for designing gain-scheduled dynamic output feedback controllers for continuous-time Linear Parameter-Varying (LPV) systems. The aim is to improve transient response by incorporating both D-stability and H∞ criteria into the synthesis conditions. We achieve this by employing changes of variables and congruence transformations, which lead to new synthesis conditions expressed as linear matrix inequalities. Additional fine-tuned scalar parameters can be used to enhance further the controller performance in terms of less conservative H∞ guaranteed costs. To assess the effectiveness of our proposed synthesis procedure, we conduct computational experiments in the context of a microinverter-based distributed power generation system. These experiments take into account real-world operational characteristics, providing a comprehensive evaluation of our approach. The results demonstrate that the designed controller effectively ensures the desired closed-loop system behavior, even when dealing with state noise and discretization errors originating from digital implementation.

Multimodel Bayesian estimation for LPV time-delay systems with incomplete observations

A multimodel Bayesian approach to identifying linear parameter-varying (LPV) systems subject to piecewise input time-delays, outliers and randomly missing observations is developed in this article. The global nonlinearity is characterized by weighted combination of multiple submodels, where each local-model identity is treated as hidden variable to represent the working mode of the system. To tackle data anomaly problems, the Student’s t-distribution is utilized to model the observations containing outliers, and the missing part of the output is regarded as another hidden variable. By introducing weighting coefficient to indicate the significance of each delay, the piecewise input time-delay can be automatically chosen irrespective of its initial interval. All required quantities, including the identities of local-model and time-delay, the missing values of the outputs, and the local-model parameters with their uncertainties, are comprehensively updated using variational Bayesian (VB) approach. Subsequently, a numerical study and the irrigation channel are adopted to prove the validity of the presented method.