Jinghao Li

Adaptive fuzzy fault-tolerant control with guaranteed tracking performance for nonlinear strict-feedback systems

In this study, we propose two backstepping-based adaptive fuzzy fault-tolerant control (FTC) methods for a class of nonlinear strict-feedback systems with actuator failures. First, a traditional FTC (TFTC) method is considered. Our analysis shows that TFTC has poor tracking performance due to the existence of approximation errors and external disturbances. Inspired by the idea that the magnitudes of control inputs decrease as the error of the last step decreases in the backstepping procedure, we propose a new prescribed performance FTC (NPP-FTC) method based on the improved error transformation technique. Compared with previous methods where only the output tracking error is guaranteed within the prescribed performance bound (PPB), we show that the state tracking error for each step between the intermediate control and virtual control remains within the PPB regardless of actuator faults. The main advantage of the NPP-FTC method is that the tracking errors and magnitudes of the control inputs can be reduced by adjusting the PPB parameters of the errors in the first and last steps. Our simulation results demonstrate the effectiveness of the proposed NPP-FTC method.

Simultaneous fault detection and control for switched linear systems with mode-dependent average dwell-time

This paper investigates the problem of the simultaneous fault detection and control (SFDC) for switched linear systems. To meet the control and detection objectives, the time-dependent detection filters and dynamic output feedback controllers are presented in SFDC under a mixed H∞/ H - framework. A mode-dependent average dwell-time (MDADT) approach, which means that each subsystem has its own average dwell time, is adopted in this paper to reduce the conservativeness of the average dwell time method. And the discretized Lyapunov function (DLF) technique is first used to relax the MDADT constraints in SFDC. Some sufficient conditions for designing filters/controllers which satisfy the H∞/ H - performance are given in terms of linear matrix inequalities (LMIs). Whats more, a two-step algorithm to solve the SFDC problem is proposed. The effectiveness of the proposed method is illustrated through two simulation examples.

Fault detection for singular switched linear systems with multiple time-varying delay in finite frequency domain

ABSTRACT This paper deals with the problem of the fault detection (FD) for continuous-time singular switched linear systems with multiple time-varying delay. In this paper, the actuator fault is considered. Besides, the systems faults and unknown disturbances are assumed in known frequency domains. Some finite frequency performance indices are initially introduced to design the switched FD filters which ensure that the filtering augmented systems under switching signal with average dwell time are exponentially admissible and guarantee the fault input sensitivity and disturbance robustness. By developing generalised Kalman–Yakubovic–Popov lemma and using Parsevals theorem and Fourier transform, finite frequency delay-dependent sufficient conditions for the existence of such a filter which can guarantee the finite-frequency H− and H∞ performance are derived and formulated in terms of linear matrix inequalities. Four examples are provided to illustrate the effectiveness of the proposed finite frequency method.

Delay-dependent adaptive dynamic surface control for nonlinear strict-feedback delayed systems with unknown dead zone

Abstract In this paper, delay-dependent adaptive dynamic surface control (DSC) is developed for a class of uncertain nonlinear time-delay systems. The considered system is in strict-feedback form with unknown dead zone. Compared with the existing results, a novel adaptive fuzzy memory state feedback controller is constructed, which relaxes the restrictions on the unknown time-delay functions and avoids the singularity problem in controller design. The unknown time delays are adaptively estimated. Design difficulties from unknown time-delay functions are overcome by using mean value theorem for differential, fuzzy logic time-delay systems, appropriate nonnegative function, and the desirable property of adaptive laws of delay parameters. A modified DSC technique is incorporated into backstepping to avoid “the explosion of complexity” problem and simplify the adaptive design procedure. By Barbalat׳s lemma, it is shown that the proposed controller can ensure that the closed-loop system is semi-globally uniformly ultimately bounded, and all the state tracking errors converge to a priori known accuracy. Finally, two simulation examples are given for showing the effectiveness of the proposed approach.

Stabilisation of descriptor Markovian jump systems with partially unknown transition probabilities

This paper is concerned with the stability and stabilisation problems for continuous-time descriptor Markovian jump systems with partially unknown transition probabilities. In terms of a set of coupled linear matrix inequalities (LMIs), a necessary and sufficient condition is firstly proposed, which ensures the systems to be regular, impulse-free and stochastically stable. Moreover, the corresponding necessary and sufficient condition on the existence of a mode-dependent state-feedback controller, which guarantees the closed-loop systems stochastically admissible by employing the LMI technique, is derived; the stabilizing state-feedback gain can also be expressed via solutions of the LMIs. Finally, numerical examples are given to demonstrate the validity of the proposed methods.

Dissipative control for a class of nonlinear descriptor systems

This paper is concerned with the dissipative control problem for a class of nonlinear descriptor systems. Based on Lyapunov stability theory, sufficient conditions are derived, which guarantee that the underlying systems are strictly dissipative. Then, the design method for a state feedback controller is provided. All the conditions can be expressed via linear matrix inequalities. Finally, a numerical example is presented to demonstrate the validity of the proposed methods.

Robust Stabilization of T–S Fuzzy Stochastic Descriptor Systems via Integral Sliding Modes

This paper addresses the robust stabilization problem for T–S fuzzy stochastic descriptor systems using an integral sliding mode control paradigm. A classical integral sliding mode control scheme and a nonparallel distributed compensation (Non-PDC) integral sliding mode control scheme are presented. It is shown that two restrictive assumptions previously adopted developing sliding mode controllers for Takagi–Sugeno (T–S) fuzzy stochastic systems are not required with the proposed framework. A unified framework for sliding mode control of T–S fuzzy systems is formulated. The proposed Non-PDC integral sliding mode control scheme encompasses existing schemes when the previously imposed assumptions hold. Stability of the sliding motion is analyzed and the sliding mode controller is parameterized in terms of the solutions of a set of linear matrix inequalities which facilitates design. The methodology is applied to an inverted pendulum model to validate the effectiveness of the results presented.

Observer-Based Fuzzy Integral Sliding Mode Control For Nonlinear Descriptor Systems

This paper investigates observer-based stabilization for nonlinear descriptor systems using a fuzzy integral sliding mode control approach. Observer-based integral sliding mode control strategies for the Takagi–Sugeno (T–S) fuzzy descriptor systems are developed. A two-step design approach is first developed to obtain the observer gains and coefficients in the switching function using linear matrix inequalities (LMIs), and the results are used to facilitate the development of a single-step design approach, which is seen to be convenient but introduces some conservatism in the design. The potential application to a class of mechanical systems is also considered. Since the descriptor system representation of mechanical systems is adopted, it is shown that in contrast to the existing fuzzy sliding mode control methods based on the normal system representation, the resulting T-S fuzzy system does not contain different input matrices for each local subsystem and the required number of fuzzy rules is consequently markedly reduced. Finally, the balancing problem of a pendulum on a car is numerically simulated to demonstrate the effectiveness of the proposed method.

Stabilisation of Discrete-Time Piecewise Homogeneous Markov Jump Linear System with Imperfect Transition Probabilities

This paper is devoted to investigating the stability and stabilisation problems for discrete-time piecewise homogeneous Markov jump linear system with imperfect transition probabilities. A sufficient condition is derived to ensure the considered system to be stochastically stable. Moreover, the corresponding sufficient condition on the existence of a mode-dependent and variation-dependent state feedback controller is derived to guarantee the stochastic stability of the closed-loop system, and a new method is further proposed to design a static output feedback controller by introducing additional slack matrix variables to eliminate the equation constraint on Lyapunov matrix. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed methods.

Fuzzy Reduced-Order Compensator-Based Stabilization for Interconnected Descriptor Systems via Integral Sliding Modes

This paper investigates the integral sliding mode control problem of T–S fuzzy interconnected descriptor system based on a reduced-order compensator. A canonical equivalent form for T–S fuzzy interconnected descriptor system is first introduced to facilitate the reduced-order compensator design. In terms of the measurable output variables of the T–S fuzzy interconnected descriptor system and the state variables of the proposed reduced-order compensator, an integral sliding mode control scheme is then developed for the T–S fuzzy interconnected descriptor system. The sliding motion is defined in the augmented space formed by the state variables of the original T–S fuzzy interconnected descriptor system and the resulting error system. It is shown that the designing parameters in the switching function can be simultaneously solved and the original T–S fuzzy interconnected descriptor system has no requirement to be relative degree one. Since the estimate error is bounded by an auxiliary dynamical system, when ideal sliding mode occurs, the resulting closed-loop system is asymptotically stable rather than uniformly ultimately bounded. Finally, a double-inverted pendulum system and a ball and beam system are numerically simulated to demonstrate the effectiveness and merits of the method proposed.