Wen Chen

A coupled method for inverse source problem of spatial fractional anomalous diffusion equations

Based on the best perturbation method, a coupled method is developed to solve the inverse source problem of spatial fractional anomalous diffusion equation. The ill-posed inverse problem is first transformed into a well-posed problem by a Tikhonov regularization algorithm. Then the corresponding direct problem is solved by the implicit difference method, in which the source term is estimated by the best perturbation method. The efficiency and the accuracy of the proposed method are demonstrated by two numerical examples.

Fault Reconstruction and Fault-Tolerant Control via Learning Observers in Takagi–Sugeno Fuzzy Descriptor Systems With Time Delays

This paper addresses the problems of observer-based fault reconstruction and fault-tolerant control for Takagi-Sugeno fuzzy descriptor systems subject to time delays and external disturbances. A novel fuzzy descriptor learning observer is constructed to achieve simultaneous reconstruction of system states and actuator faults. Sufficient conditions for the existence of the proposed observer are explicitly provided. Utilizing the reconstructed fault information, a reconfigurable fuzzy fault-tolerant controller based on the separation property is designed to compensate for the impact of actuator faults on system performance by stabilizing the closed-loop system. In addition, the design of the fault reconstruction observer and the fault-tolerant controller is formulated in terms of linear matrix inequalities that can be conveniently solved using convex optimization techniques. Finally, simulation results on a truck-trailer system are presented to verify the effectiveness of the proposed approaches.

A novel fault reconstruction approach to satellite attitude control system via learning unknown input observer and H ∞ techniques

A novel robust fault reconstruction approach is proposed for satellite attitude control systems (ACS) by proposing a learning unknown input observer (LUIO). Stability of LUIO and ultimately boundedness of dynamic fault deviation are proved using Lyapunov stability analysis. LUIO design problem can be solved effectively using MATLAB LMI toolbox. Finally, mathematical simulation on satellite closed-loop ACS demonstrates the effectiveness of the proposed approach.

Integrated design of fault reconstruction and fault-tolerant control against actuator faults using learning observers

ABSTRACT This paper addresses the problem of integrated fault reconstruction and fault-tolerant control in linear systems subject to actuator faults via learning observers (LOs). A reconfigurable fault-tolerant controller is designed based on the constructed LO to compensate for the influence of actuator faults by stabilising the closed-loop system. An integrated design of the proposed LO and the fault-tolerant controller is explored such that their performance can be simultaneously considered and their coupling problem can be effectively solved. In addition, such an integrated design is formulated in terms of linear matrix inequalities (LMIs) that can be conveniently solved in a unified framework using LMI optimisation technique. At last, simulation studies on a micro-satellite attitude control system are provided to verify the effectiveness of the proposed approach.

Fault reconstruction and accommodation in linear parameter-varying systems via learning unknown-input observers

This paper addresses the problem of observer-based fault reconstruction and accommodation for polytopic linear parameter-varying (LPV) systems. A polytopic representation of an LPV system subject to actuator faults and external disturbances is first established; then, a novel polytopic learning unknown-input observer (LUIO) is constructed for simultaneous state estimation and robust fault reconstruction. The stability of the presented LUIO is proved using Lyapunov stability theory together with H∞ techniques. Further, using reconstructed fault information, a reconfigurable fault-tolerant controller is designed to compensate for the influence of actuator faults by stabilizing the closed-loop system. At last, an aircraft example is employed to illustrate the effectiveness and practicability of the proposed techniques.

Robust Fault Reconstruction in Discrete-Time Lipschitz Nonlinear Systems via Euler-Approximate Proportional Integral Observers

The problem of observer-based robust fault reconstruction for a class of nonlinear sampled-data systems is investigated. A discrete-time Lipschitz nonlinear system is first established, and its Euler-approximate model is described; then, an Euler-approximate proportional integral observer (EPIO) is constructed such that simultaneous reconstruction of system states and actuator faults are guaranteed. The presented EPIO possesses the disturbance-decoupling ability because its architecture is similar to that of a nonlinear unknown input observer. The robust stability of the EPIO and convergence of fault-reconstructing errors are proved using Lyapunov stability theory together with techniques. The design of the EPIO is reformulated into convex optimization problem involving linear matrix inequalities (LMIs) such that its gain matrices can be conveniently calculated using standard LMI tools. In addition, to guarantee the implementation of the EPIO on the exact model, sufficient conditions of its semiglobal practical convergence are provided explicitly. Finally, a single-link flexible robot is employed to verify the effectiveness of the proposed fault-reconstructing method.

A new strategy for fault estimation in Takagi-Sugeno fuzzy systems via a fuzzy learning observer

This paper is to suggest a new strategy for fault estimation in Takagi-Sugeno (T-S) fuzzy systems. A fuzzy Learning Observer (FLO) is constructed to achieve simultaneous estimation of system states and actuator faults. The FLO is able to estimate both constant and time-varying faults accurately, and a systematic method is also proposed to select gain matrices for the FLOs. Stability and convergence of the proposed observer is proved using Lyapunov stability theory. The design of FLOs can be formulated in terms of Linear Matrix Inequalities (LMIs) that can be conveniently solved using LMI optimization technique. A single-link flexible manipulator is employed to verify the effectiveness of the proposed fault-estimating approaches.

Fault reconstruction for Takagi–Sugeno fuzzy systems via learning observers

ABSTRACT This paper addresses the problem of observer-based fault reconstruction for Takagi–Sugeno fuzzy systems. Two types of fuzzy learning observers are constructed to achieve simultaneous reconstruction of system states and actuator faults. Stability and convergence of the proposed observers are proved using Lyapunov stability theory, and necessary conditions for the existence of the observers are further discussed. The design of fuzzy learning observers can be formulated in terms of a series of linear matrix inequalities that can be conveniently solved using convex optimisation technique. A single-link flexible manipulator is employed to verify the effectiveness of the proposed fault-reconstructing approaches.

Design of novel observers for robust fault detection in discrete-time Lipschitz non-linear systems with Euler-approximate models

This paper addresses the problem of observer-based robust fault detection in a class of Lipschitz non-linear systems. A Euler-approximate model for continuous-time Lipschitz non-linear systems is first established; then, a discrete time non-linear observer is designed such that the dynamic output-estimation error, which is assigned as a residual signal, asymptotically converges to zero if no actuator faults and external disturbances exist in the system. The new observer has similarity to a non-linear unknown input observer (UIO). Compared with the existing UIOs, the design of the presented observer requires fewer gain matrices and equation constraints; less computation load is therefore needed. On the other hand, the new observer is designed based on the Euler-approximate model. To ensure its implementation on the exact model, sufficient conditions for semiglobal practical convergence of the proposed observer are explicitly provided. With external disturbances, a nonlinear H∞ observer is constructed to achieve robust actuator fault detection. Observer design problem can be systematically solved using linear matrix inequality (LMI)-based optimisation technique. Lastly, a single-link flexible robot is employed to illustrate the effectiveness of the proposed observer-based FD scheme.

Robust iterative learning control synthesized with sliding-mode control for output tracking

This paper is to propose a new design of Iterative learning Control (ILC) for the purpose of output tracking. The novelty lies in the synthesis of ILC with sliding-mode control such that the tracking performance and accuracy can be improved. The considered system is first transformed into two subsystems such that the new design can be applied to broad systems. Based on the transformed systems, an ILC is designed for the first-order derivative of the control signal, instead of the control signal itself. The variable structure functions are therefore integrated such that the chattering can be eliminated accordingly. The convergence of the output-tracking error is also proved. The effectiveness of the new ILC for output tracking is verified in a simulation study.