Ding Zhai

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 multiple time-delay systems with application to electrical circuit

Abstract In this paper, an H − / H ∞ fault detection (FD) filter is designed for linear singular systems with multiple state delays. System faults and unknown disturbances are assumed to reside in finite frequency ranges. By combining the Parseval theorem and the strict S-procedure, both time domain and frequency domain approaches are used to formulate a new delay-dependent finite frequency bounded real lemma (BRL), which includes some existing results as special cases. Based on the obtained BRL, convex FD filter design conditions are derived in terms of solving a set of linear matrix inequalities (LMIs). The effectiveness of the proposed finite frequency FD method is illustrated through a simulation example on the electrical circuit.

Prescribed Performance Switched Adaptive Dynamic Surface Control of Switched Nonlinear Systems With Average Dwell Time

In this paper, the problem of adaptive fuzzy tracking control is investigated for a class of switched nonlinear systems. A new switched adaptive output feedback control method is presented where the changes of plant can be considered explicitly. Mode-dependent fuzzy logic systems are employed to approximate the switching nonlinear functions in system. To reduce the conservativeness caused by adoption of a common adaptive law for all subsystems, the switching optimal weight vectors are directly estimated via switched adaptive laws at each step of backstepping. However, the difficulties are how to ensure the estimation performance subject to persistent switchings, and how to design common virtual controls based on switching parameters. Further, based on the estimation of optimal weight vectors, the switched fuzzy state observer can be also applied to obtain the unmeasured states. By designing a novel Lyapunov function, the improved dynamic surface control incorporated by prescribed performance technique guarantees all the total state tracking errors, not partial ones, within predefined performance bounds. Simulation results are provided to demonstrate the effectiveness of the proposed method.

Simultaneous H2/H∞ fault detection and control for networked systems with application to forging equipment

This paper investigates the simultaneous fault detection and control (SFDC) problems for a class of discrete-time networked systems with multiple stochastic delays and data missing. Both faults and disturbances are assumed to be in low frequency domain. The communication delays are uniformly modeled by multiple random variables obeying the Bernoulli distributions, which are mutually correlated by a prior Pearson correlation coefficient matrix. Then the closed-loop system is formulated as a special jump linear system. The generalized definitions of the H2 and H ∞ indexes for such underlying systems are proposed to measure the detection and control performances, respectively. Then a mixed H 2 / H ∞ SFDC approach is proposed to achieve the desired detection and control objectives. To cope with the H2 performance index in a given frequency range directly, by Parseval lemma and S-procedure, a relaxed condition is presented to reduce the conservatism of the existing results. And the integrated detector/controller is derived in terms of solving a set of linear matrix inequalities (LMIs). The developed method is applied to the large forging equipment drive systems, and simulation results demonstrate the effectiveness of the results. HighlightsRandom delays is uniformly represented by multiple correlated Bernoulli processes.A more relaxed condition is presented to satisfy the generalized H 2 performance.A novel model is proposed to represent communication delays and measurement missing.

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.

Switched Adaptive Fuzzy Tracking Control for a Class of Switched Nonlinear Systems Under Arbitrary Switching

This paper deals with the problem of adaptive tracking control for a class of switched uncertain nonlinear systems under arbitrary switching. First, combing fuzzy approximation and dynamic surface control (DSC), a switched adaptive state-feedback control scheme is proposed based on directly tuning the estimation of the switching ideal weight vectors in fuzzy logic systems. Switched adaptive laws and switched first-order filters in DSC are designed at each step in the backstepping to reduce the conservativeness caused by adoption of common adaptive laws and filters for each subsystem. By constructing a novel common Lyapunov function, the boundedness of the closed-loop system is ensured, while the tracking error converges to a small neighborhood of the origin. Next, based on the estimation of ideal weight vectors, the proposed adaptive control scheme is extended to the output-feedback case where a switched fuzzy observer is first proposed to estimate the unmeasured states. The main advantage of the developed adaptive control schemes is that the changes of plant can be considered explicitly due to switching, which contributes to less conservativeness of the designed controllers. Finally, two simulation results illustrate the effectiveness of the proposed schemes.

Dynamic output feedback H∞ control for switched T-S fuzzy systems via discretized Lyapunov function technique

This paper investigates the problem of the dynamic output feedback H ∞ control for a class of switched T-S fuzzy systems. Based on the mode-dependent average dwell time method and discretized Lyapunov function technique (DLF), a new method is proposed to analyze the stability for the switched fuzzy systems with unstable subsystems. In addition, by using the switched parallel distributed compensation scheme, a new membership-function-dependent switching law for the controllers is constructed. Then, the dynamic output feedback controller design for the switched systems with time-dependent switching law is proposed based on the DLF technique. Finally, sufficient conditions of the existence of the dynamic output feedback controller are proposed and formulated in the form of linear matrix inequalities (LMIs). The effectiveness of the proposed method is illustrated through three simulation examples.

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.

Stability analysis and state feedback control of continuous-time T-S fuzzy systems via anew switched fuzzy Lyapunov function approach

This paper deals with stability analysis and control design problems for continuous-time Takagi-Sugeno (T-S) fuzzy systems. First, a new membership-function-dependent switching law is proposed and a relaxation parameter is introduced into this switching law to guarantee a minimal dwell time between two consecutive switching. Compared to the existing methods, the most important point is that with the help of the dwell time, the discretized Lyapunov function (DLF) technique can be adopted. Then a new stability criterion of the T-S fuzzy system with less conservatism is derived based on a fuzzy discretized Lyapunov function (FDLF). Second, to estimate the domain of attraction (DA), an algorithm with less iteration steps is proposed. Based on the proposed switching method, sufficient conditions for existence of the state feedback controllers are presented via the switched non-parallel distributed compensation (non-PDC) scheme. The effectiveness of the proposed method is illustrated through three simulation examples.