Linear Parameter-varying Systems Research Articles

Q‐learning‐based H∞ control for LPV systems

AbstractIn this paper, a model‐free H∞ control method is developed for discrete‐time linear parameter‐varying (LPV) systems by leveraging Q‐learning, which employs the data encompassing system states, control inputs, exogenous disturbance, and time‐varying convex hull rather than the dynamical model known a priori. A policy iteration algorithm presented via linear matrix inequality formed by such collected data is developed with convergence guarantee. Our analysis demonstrates that, in the presence of sufficiently rich disturbances, the attenuation level converges to a lower value than the traditional H∞ control solution derived from an exact LPV model. A numerical example is demonstrated to verify the stabilization, disturbance attenuation, adaptivity, and convergence of the H∞ attenuation level. Moreover, a continuous stirred tank reactor (CSTR) approximated by a discrete‐time LPV system is employed to show the practical potential of the developed model‐free approach.

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.

Stability and Robustness Analysis and Optimization for Gain-Scheduled Control of Aero-Engines

Abstract Gainscheduled control is widely applied in the aerospace domain, yet the selection of design points for gainscheduling controllers to ensure stability and robustness throughout the range of scheduling variables remains theoretically unguided. Therefore, this paper introduces an analysis and optimization method for the stability and robustness of gain-scheduled control, aimed at providing a theoretical framework for design points selection. Initially, the method characterizes the gainscheduled control system as a polytopic Linear Parameter Varying (LPV) system, wherein the design points of the gainscheduled control system correspond to the vertices of the polytopic LPV system. Subsequently, the method utilizes Linear Matrix Inequality techniques to demonstrate the stability of a polytopic LPV system with a corresponding number of vertices, and by assessing the approximation degree between the polytopic LPV system and the gainscheduled control system with an identical number of design points, it evaluates and ensures the stability of the latter, thereby establishing the minimal requirements for the number of design points. After ensuring stability, the method further refines the number of design points within the gainscheduled control system to meet additional robustness and performance considerations. A case study on turbofan engine controls validates the proposed method. New design points, selected via stability and robustness analysis, enhance the system's steadystate phase margin and robustness against model uncertainties. Moreover, compared to a vgap metric-based method, the two methods exhibit similar performance in terms of stability, robustness, and tracking control. However, the proposed method requires fewer design points, resulting in less conservatism.

Sampled-data static output feedback robust MPC for LPV systems with bounded disturbances

This paper investigates a sampled-data static output feedback robust model predictive control (MPC) approach for continuous-time linear parameter varying (LPV) systems with unknown system states and bounded disturbances. Between two successive sampling time instants, it is assumed that the controlled LPV systems evolve in continuous-time, and the control inputs are piecewise constant. The robust stability conditions and control input constraints on the closed-loop system are considered in the formulated robust MPC optimization. The constraints in the formulated robust MPC optimizations are formulated as linear matrix inequalities (LMIs) and solved as convex optimization. The designed sampled-data static output feedback robust MPC optimization has a simple structure and directly optimizes output feedback controller. Furthermore, the system state constraint sets are on-line updated over the sampling interval. The designed sampled-data static output feedback robust MPC approach has the property of recursive feasibility, and can guarantee robust stability of the controlled continuous-time LPV systems. A simulation example is given to illustrate the effectiveness of the approach.

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

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

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.

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.

A robust [formula omitted] fault-tolerant control approach for time-delay LPV systems with uncertain parameters and unknown disturbances

The article proposes a H∞ fault-tolerant control approach for a series of uncertain linear parameter-varying (LPV) time-delay models to obtain disturbance suppressions. Specifically, by applying the Lyapunov functions, a series of feedback controllers are provided to ensure the robust performance of LPV models with actuator faults. Meanwhile, a convex optimization strategy is developed for resolving optimization problems in the presence of bilinear matrix inequalities (BMIs), where the robustness conditions are improved to guarantee the stability of LPV model under uncertain factors. By resolving a class of linear matrix inequalities (LMIs), the gain matrices for LPV systems can be obtained. Furthermore, the less conservative conditions are developed and supported by strict theoretical derivation. Ultimately, the validity of proposed approach is confirmed by simulation analyses of truck–trailer systems.

Estimation of Crosswind Disturbances for a Vehicle by LPV‐MHE and its Application to Disturbance Cancellation

Crosswinds and transverse slopes of the road surface affect the motion of a ground vehicle as disturbances. The objective of this paper is to develop a method for estimating crosswind disturbances and lateral force disturbances caused by transverse slopes of the road surface under the variation of the vehicle speed. Firstly, a dynamical model of a vehicle is described as a Linear Parameter‐Varying (LPV) system in which the value of the coefficient matrices vary with the vehicle velocity. Then, an algorithm to estimate the disturbance is derived based on Moving Horizon Estimation (MHE) and applied to the derived LPV system. Furthermore, a simple control law which counteracts the effects of the disturbances on the lateral velocity and the yaw rate in steady‐state based on the estimates of the disturbances is presented. The effectiveness of the proposed method is demonstrated by a numerical example. © 2024 The Author(s). IEEJ Transactions on Electrical and Electronic Engineering published by Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

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.

Safe Reinforcement Learning via a Model-Free Safety Certifier.

This article presents a data-driven safe reinforcement learning (RL) algorithm for discrete-time nonlinear systems. A data-driven safety certifier is designed to intervene with the actions of the RL agent to ensure both safety and stability of its actions. This is in sharp contrast to existing model-based safety certifiers that can result in convergence to an undesired equilibrium point or conservative interventions that jeopardize the performance of the RL agent. To this end, the proposed method directly learns a robust safety certifier while completely bypassing the identification of the system model. The nonlinear system is modeled using linear parameter varying (LPV) systems with polytopic disturbances. To prevent the requirement for learning an explicit model of the LPV system, data-based λ -contractivity conditions are first provided for the closed-loop system to enforce robust invariance of a prespecified polyhedral safe set and the system's asymptotic stability. These conditions are then leveraged to directly learn a robust data-based gain-scheduling controller by solving a convex program. A significant advantage of the proposed direct safe learning over model-based certifiers is that it completely resolves conflicts between safety and stability requirements while assuring convergence to the desired equilibrium point. Data-based safety certification conditions are then provided using Minkowski functions. They are then used to seemingly integrate the learned backup safe gain-scheduling controller with the RL controller. Finally, we provide a simulation example to verify the effectiveness of the proposed approach.