Linear Parameter-varying Systems Research Articles

A novel geometry optimization strategy to online active fault diagnosis of LPV systems

This paper proposes a novel geometry optimization strategy for the online robust active fault diagnosis (AFD) of discrete-time linear parameter varying (LPV) systems under set-theoretic framework. By establishing a bank of zonotopic set-value observers to match healthy/faulty system modes, the key of the optimization strategy comes down to the design of the optimal system inputs and gain matrices simultaneously. The criterion on the design of optimal inputs is characterized by fully utilizing the geometry property of zonotopes, which formulates a non-convex fractional programming problem able to be solved under 0–1 mixed integer quadratic programming framework based on a series of transformations. While the optimal gain matrices can be obtained analytically based on a so-called zonotopic kalman filtering process. The proposed method can improve the sensitivity of AFD as much as possible while ensuring the stability of the designed observer. At the end, two physical models are used to verify the effectiveness of our proposed method.

Design of a mixed ℋ2/ℋ∞ gain scheduling state derivative feedback controller for linear parameter-varying systems

In this paper, the mixed guaranteed cost for continuous-time linear parameter-varying (LPV) systems is proposed. In addition, the gain scheduling (GS) strategy and the state derivative feedback (SDF) were considered. The time-varying parameter is assumed to be available for online measurement, and the conditions are based on linear matrix inequalities (LMIs). To improve the behaviour of the system, the -stability is used. Examples show that the proposed conditions achieved good results in reducing the disturbance effect in the system. Furthermore, with the proposed methods, it is possible to guarantee the asymptotic stability and a mixed guaranteed cost minimisation.

Active Fault Diagnosis for LPV Systems: An Index-Based Approach

This article investigates the active fault diagnosis (AFD) problem for linear parameter-varying (LPV) systems. The system uncertainties, including system disturbances, noises, and initial conditions, are characterized by uncertain Gaussian zonotopes (UGZs). An index-based AFD scheme is proposed, which can avoid the requirement of complete separation of output sets of different system modes and reduce conservatism to a certain extent. A new index is proposed to characterize the similarity between two zonotopes. According to this index, the auxiliary input is designed by solving a quadratic programming problem. A novel fault diagnosis strategy is proposed to determine which mode the system is actually operating in. A numerical example is presented to demonstrate the effectiveness of the proposed approach.

On Robust Stabilization of Discrete-Time LPV/LFR Systems

This technical article presents novel robust stabilization conditions for discrete-time linear parameter-varying (LPV) systems with linear fractional representation (LFR). The proposed conditions rely on the use of slack variables and decision matrices associated with the LFR approach to provide new controller designs. In addition, we address parameter-dependent Lyapunov functions and full-block multipliers to obtain less conservative synthesis conditions for discrete-time LPV/LFR systems. Design conditions are cast in the form of linear matrix inequalities to generate robust state-feedback and output-feedback controllers. Numerical examples demonstrate the effectiveness of the proposed method.

Design of switching state-feedback controllers for linear systems subject to asymmetric saturations*

This paper considers the problem of controlling a linear system affected by asymmetrical input saturation. The proposed solution is based on using a linear matrix inequality (LMI)-based methodology to find the gains of a switching state-feedback controller. The main difference and contribution when compared to existing approaches is that the switching rule is chosen based on the closed-loop performance that each of the non-saturating controller gains can achieve when used with the current value of the state vector. Although the main focus of the paper is on time-invariant systems, the possible extension to linear parameter-varying (LPV) systems is discussed. An illustrative example is used to show the main features of the proposed approach.

Dynamic-Memory Event-Based Asynchronous Attack Detection Filtering for a Class Of Nonlinear Cyber-Physical Systems.

In this article, we endeavor to address the problem of asynchronous attack detection for a class of nonlinear cyber-physical system (CPS) under the dynamic-memory event-triggered transmission protocol (DMETP). Malicious attacks under consideration are composed of the parameter-dependent false data-injection (FDI) attacks and the multichannel deception attacks with the time delay. Meanwhile, we attempt to employ the T-S fuzzy singular Semi-Markov jump linear parameter-varying (SS-MJLPV) systems to describe the stochastic jump characteristics and nonlinear time-varying characteristics of CPSs. Then, the DMETP is proposed for the first time, which can not only relieve the bandwidth pressure but also obtain the key released packets at the crest or trough of the curve. By augmenting the states of the original system and the asynchronous attacks detection filter, the issue of attacks detection is converted into an auxiliary dissipative filtering for the CPS. Moreover, sufficient conditions for the existence of the attacks detection filter are obtained. Finally, the effectiveness of the proposed scheme is verified via the networked truck-trailer reversing system.

Direct data-driven LPV control of nonlinear systems: An experimental result

We demonstrate that direct data-driven control of nonlinear systems can be successfully accomplished via a behavioral approach that builds on a Linear Parameter-Varying (LPV) system concept. An LPV data-driven representation is used as a surrogate LPV form of the data-driven representation of the original nonlinear system. The LPV data-driven control design that builds on this representation form uses only measurement data from the nonlinear system and a priori information on a scheduling map that can lead to an LPV embedding of the nonlinear system behavior. Efficiency of the proposed approach is demonstrated experimentally on a nonlinear unbalanced disc system showing for the first time in the literature that behavioral data-driven methods are capable to stabilize arbitrary forced equilibria of a real-world nonlinear system by the use of only 7 data points.

Zonotopic Set-Membership State Estimation for Switched LPV Systems

This paper addresses the state estimation problem for switched discrete-time Linear Parameter Varying (LPV) systems with mensurable and unmeasurable scheduling parameters. A zonotopic switched polytopic state estimator, considering parameter uncertainty, is proposed based on a Set-Membership Approach (SMA). Taking Average Dwell Time (ADT) into account, a new criterion is proposed to guarantee the convergence of the estimation. An application to vehicle lateral dynamics state estimation is used as case study. Simulation results reveal the effectiveness of the proposed algorithm and demonstrate advantages over the existing methods.

Gain-Scheduled Control of LPV Systems with Structural Constraints

In large-scale dynamic systems, consisting of the interconnection of several subsystems, the control law must obey a certain distributed structure defined by the information exchange pattern on a communication network. In case the system exhibits parameters which vary over time, the Linear Parameter Varying (LPV) paradigm provides a control-oriented framework for the design of robust or gain-scheduled control laws. Since each subsystem has only access to a partial knowledge of the overall set of parameters, due to the constraint imposed by the communication network, the controller gain must satisfy some structural constraints which increase the complexity of the design problem. This paper proposes a novel approach based on Linear Matrix Inequalities (LMIs) to deal with the distributed control of large-scale systems described by a LPV dynamics. LMI conditions are established for the design of a gain-scheduled controller ensuring exponential stability of the overall system with a prescribed decay rate, while satisfying the structural constraints imposed by the communication network. A simulation case study is presented to show the effectiveness of the proposed approach.

Distributed set-membership state estimation based on a zonotope method for linear parameter-varying systems

Distributed set-membership state estimation based on a zonotope method for linear parameter-varying systems

LMI-based Data-Driven Robust Model Predictive Control

Predictive control, which is widely used currently, bases on a model of the system to compute the applied input optimizing the future system behavior. If the nominal models are not given or are uncertain, data-driven model predictive control approaches can be employed, where control input is directly obtained from past measured trajectories. Using a data informativity framework and Finsler's lemma, we propose a data-driven robust linear matrix inequality-based model predictive control scheme that considers input and state constraints for linear parameter-varying systems and Lur'e-type nonlinear systems. Using these data, we formulate the problem as a semi-definite optimization problem, whose solution provides the matrix gain for the linear feedback, while the decisive variables are independent of the length of the measurement data. The designed controller stabilizes the closed-loop system asymptotically and guarantees constraint satisfaction. Numerical examples are conducted to illustrate the method.

A Kernel-Based Identification Approach to LPV Feedforward: With Application to Motion Systems

The increasing demands for motion control result in a situation where Linear Parameter-Varying (LPV) dynamics have to be taken into account. Inverse-model feedforward control for LPV motion systems is challenging, since the inverse of an LPV system is often dynamically dependent on the scheduling sequence. The aim of this paper is to develop an identification approach that directly identifies dynamically scheduled feedforward controllers for LPV motion systems from data. In this paper, the feedforward controller is parameterized in basis functions, similar to, e.g., mass-acceleration feedforward, and is identified by a kernel-based approach such that the parameter dependency for LPV motion systems is addressed. The resulting feedforward includes dynamic dependence and is learned accurately. The developed framework is validated on an example.

Finite-time control for discrete-time nonlinear Markov switching LPV systems with DoS attacks

This work studies the finite-time control problem for discrete-time nonlinear Markov switching linear parameter varying (LPV) systems with denial-of-service (DoS) attacks. The aperiodic DoS attacks are introduced into the systems with partially unknown transition probabilities. First, considering the characteristics of aperiodic DoS attacks, an appropriate feedback controller is designed according to that whether it is attacked or not. Furthermore, the finite-time stability criteria of closed-loop system are derived by means of iterative technique and multiple Lyapunov functions. Finally, a turbofan engine model is taken as an example to verify the effectiveness and feasibility of the proposed finite-time control method.

DMVT-based observer design for general affine class of fractional-order nonlinear MIMO systems

In this article, a new observer design technique is proposed for the general affine class of fractional-order nonlinear multi-input/multi-output (MIMO) systems. This study is presented based on the differential mean value theorem. One significant characteristic of the suggested approach is that the nonlinear dynamic of observer error is converted into a linear parameter-varying system. Stability and convergence of observation error are shown using the Lyapunov direct method leading to feasibility and existence of a solution for some linear matrix inequalities. The performance and efficacy of the proposed method are evaluated through some illustrated simulations.

Formula omitted] gain-scheduled state-feedback design with experimental validation in a control moment gyroscope represented as a polynomial LPV model

The main contribution of this paper is a new H2 gain-scheduled state-feedback synthesis condition for continuous-time linear parameter-varying (LPV) systems where the parameters have bounded rates of variation. The matrices of the model as well as the control gain can have arbitrary polynomial dependence on the time-varying parameters. The synthesis conditions are formulated in terms of LMI relaxations combined with a search in a bounded scalar parameter, which can be used to obtain controllers with improved performance. As an experimental validation of the results, gain-scheduled controllers are designed and applied to a control moment gyroscope modeled as an LPV system with polynomial dependence on the time-varying parameters. Comparisons with a time-invariant controller, designed with the same performance criterion, are presented to illustrate the advantages of the proposed approach.

Robust observer design for LPV systems using Kronecker sum and direct searching

This paper addresses a robust Luenberger observer for an uncertain linear parameter varying (LPV) system based on the concepts of direct searching, Kronecker sum, and small gain theorem. An algorithm is proposed to investigate the situation of the different parts of the initial observer design space, in terms of suitability for being selected as the observer gain or needing elimination due to being an undesirable part. To find the undesirable parts of the design space, the singularity of the Kronecker sum matrix of the estimation error is checked by employing the small gain theorem concept. By excluding undesired parts from the entire design space and checking the remaining parts’ feasibility, a suitable solution can be found, appropriately. The performance of the proposed observer design method is illustrated by using numerical examples and an electric ground vehicle (EGV) system for the estimation of the vehicle sideslip angle and the yaw rate. The results prove the appropriateness of the designed observer using the proposed approach.

Robust Stability Analysis of Linear Parameter-Varying Systems With Markov Jumps

This article presents conditions to assure the mean-square stability of linear parameter-varying systems with Markov jumps. The model dynamics are driven not only by a Markov chain but also by time-varying parameters that take values in a polytopic set. No assumption is imposed on how the parameters vary within the polytopic set, i.e., the variation rate can be arbitrarily fast. The proposed conditions stem from a homogeneous polynomial Lyapunov function in the state space, adapted to account for Markov jumps. The stability certificate is sought through linear matrix inequalities. Numerical examples illustrate this article’s contribution.

Observer-Based Control for Continuous-Time Switched Linear Parameter-Varying Systems

Observer-Based Control for Continuous-Time Switched Linear Parameter-Varying Systems

Sampled-Data Linear Parameter Variable Approach for Voltage Regulation of DC–DC Buck Converter

This paper addresses the new method for output voltage regulation of DC–DC buck converter nonlinear systems by a sampled-data linear parameter varying (LPV) controller. For this purpose, an output-error state-space affine LPV model is presented for DC–DC buck converter nonlinear systems. The sampled-data structure of the controller is considered as a time delay in the input, and stabilization conditions are obtained for LPV systems with affine dependence on the parameter by using a parameter-dependent Lyapunov–Krasovskii functional. Then, the design condition of the sampled-data LPV controller with an appropriate sampling period is derived to guarantee that the output voltage of the DC–DC buck converter can be adjusted to the desired voltage. Finally, simulation results are provided to show the validity of the presented approach in practical control applications where there are limitations on the value of the sampling period and the cost of the digital implementation.

A Survey of Output Feedback Robust MPC for Linear Parameter Varying Systems

For constrained linear parameter varying (LPV) systems, this survey comprehensively reviews the literatures on output feedback robust model predictive control (OFRMPC) over the past two decades from the aspects on motivations, main contributions, and the related techniques. According to the types of state observer systems and scheduling parameters of LPV systems, different kinds of OFRMPC approaches are summarized and compared. The extensions of OFRMPC for LPV systems to other related uncertain systems are also investigated. The methods of dealing with system uncertainties and constraints in different kinds of OFRMPC optimizations are given. Key issues on OFRMPC optimizations for LPV systems are discussed. Furthermore, the future research directions on OFRMPC for LPV systems are suggested.