Fault estimation and fault tolerant control for interval type-2 Takagi–Sugeno fuzzy systems via membership-function-dependent approach

Abstract

This paper investigates the fault estimation (FE)-based fault tolerant control (FTC) technique to achieve the desired control performance for the nonlinear systems suffering from uncertainties, external disturbance and actuator faults using the interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy model. In this work, an IT2 fuzzy observer is built to simultaneously estimate both the system states and actuator faults, upon which a fault tolerant controller is proposed to guarantee the asymptotical stability of the closed-loop system with a prescribed $$H_{\infty }$$ H ∞ performance level. Considering the bidirectional robustness interactions between the observer and FTC system, an integrated design technique is developed to address observer and FTC units together in one step to realize the required robustness within the whole closed-loop FTC system. By utilizing Lyapunov stability theory combined with the matrix inequality convexification techniques, a membership-function-dependent (MFD) FTC strategy is proposed where the information of membership functions is taken into account in the analysis for relaxation of the stability conditions. Additionally, to offer greater design flexibility and lower implementation cost to the fault tolerant controller, the imperfect premise matching (IPM) scheme is adopted, such that the premise membership functions of the fault tolerant controller can be chosen differently from those of IT2 fuzzy model. Finally, simulation results are provided to validate the effectiveness of the proposed FTC strategy.

Decentralized Fuzzy Fault Estimation Observer Design for Discrete-Time Nonlinear Interconnected Systems

“…Among them, fuzzy fault estimation using Takagi-Sugeno (T-S) fuzzy model [25] has the advantage of being able to easily achieve fault estimation for nonlinear systems [26]. Thus, many remarkable studies on fuzzy fault estimation are being presented as follows [27][28][29][30][31][32][33][34][35][36]: In [28,29], the continuous-and discrete-time fault estimation techniques have been presented for T-S fuzzy systems, respectively. In [27,[33][34][35], the various problems have been solved for the fuzzy fault estimation for IT2 fuzzy systems.…”

“…Thus, many remarkable studies on fuzzy fault estimation are being presented as follows [27][28][29][30][31][32][33][34][35][36]: In [28,29], the continuous-and discrete-time fault estimation techniques have been presented for T-S fuzzy systems, respectively. In [27,[33][34][35], the various problems have been solved for the fuzzy fault estimation for IT2 fuzzy systems. In [31], the fault estimation problems have been addressed for nonlinear fractional-order systems with unknown inputs.…”

Membership function‐dependent predictive control for interval type‐2 Takagi–Sugeno fuzzy system

“…The results of the MFD obtained through staircase function approximation for the upper and lower MFs are presented in Wang and Ma [23]. Based on MFD techniques, an investigation has been conducted on fault estimation and fault‐tolerant control, as described in Zhou et al [24]. The results demonstrate that compared to scenarios where the information of MFs has not been introduced, better control effectiveness and reduced conservatism are achieved.…”

Fault‐tolerant control design for stochastic distribution control systems based on k‐step fault estimation

“…Over the past several decades, fault estimation techniques based on observer theory have been extensively studied [13–15, 17, 18], including adaptive observer [14], descriptor observer [17], high‐gain observer [18], and so on. The matched actuator fault and system state was estimated by an adaptive fuzzy observer and the FE information was applied to compensate the effect of fault [19]. In Hamdi et al [20], the reconstruction of the actuator fault for the linear parameter varying system was performed by using a sliding mode observer.…”