Decentralized adaptive fault-tolerant control for large-scale systems with external disturbances and actuator faults

Abstract

This paper investigates the decentralized adaptive fault-tolerant control problem for a class of uncertain large-scale interconnected systems with disturbances and actuator faults including stuck, outage and loss of effectiveness. It is assumed that the upper bounds of the disturbances and stuck faults are unknown. The considered disturbances and unknown interconnections contain matched and mismatched parts. A decentralized adaptive control scheme with backstepping method is developed. Then, according to the information from the adaptive mechanism, the effects of both the actuator faults and the matched parts of disturbances and interconnections can be eliminated completely. Furthermore, cyclic-small-gain technique is introduced to address the mismatched interconnections such that the resulting closed-loop system is asymptotically stable with disturbance attenuation level $\gamma$. Compared with the existing results, disturbance rejection property can be guaranteed for each subsystem. Finally, a simulation example of a large-scale power system is provided to show the effectiveness of the proposed approach.

Introduction

Decentralized control for large-scale interconnected systems has received considerable attention, due to its applications in broad areas including manufacturing, power systems, telecommunication networks, and so on. The main reasons motivating decentralized control design are summarized as follows: (i) due to the high dimensionality of large-scale systems, it is difficult to design a single centralized controller; and (ii) if some subsystems are distributed distantly, it is difficult for a centralized controller to gather feedback signals from these subsystems. Thus, the main advantages of decentralized control are the avoidance of computational complexity and the reduction of economic costs. One of the basic problems arising in the decentralized control design is how to handle the interconnections among different subsystems.

Disturbances are always inevitable in many practical applications. Therefore, the robustness of decentralized controller design with respect to disturbances becomes a critical issue. For linear large-scale systems, Veillette, Medanić, and Perkins (1992) proposed a decentralized $H_{\infty }$ controller design method by using a modified Riccati equation approach. For nonlinear large-scale systems, Yang and Wang (1999) developed a decentralized $H_{\infty }$ controller design approach, and the controller design conditions were given in the formulation of solutions of Hamilton–Jacobi inequalities. In Jiang, Repperger, and Hill (2001) and Jiang (2002), the problem of decentralized output-feedback stabilization/tracking with disturbance attenuation was considered, where the common matching and growth conditions were relaxed. Apart from the aforementioned approaches, decentralized adaptive control schemes (Ioannou, 1986) have been applied to address the decentralized control problem Wen (1994), Wen et al. (2009). However, actuator faults were not taken into account in the above results.

Actuator faults generally result in poor system performance or even cause the instability. For this reason, the research on fault-tolerant control (FTC) design for dynamic systems has attracted considerable attention. Fruitful results have been made based on various approaches such as robust control-based FTC schemes (Khosrowjerdi, Nikoukhah, & Safari-Shad, 2004), diagnosis-based approaches (Gao & Ding, 2007), and adaptive actuator fault compensation schemes (Wang & Wen, 2010). Despite these efforts, the existing results on fault-tolerant design mainly focus on centralized control systems. It is only in recent years that considerable research efforts have been made with respect to the decentralized FTC of large-scale systems. To name a few, in Wang, Wen, and Yang (2009), the decentralized stabilization of interconnected systems with outage-actuator faults was investigated. In Li and Yang (2017), decentralized adaptive backstepping control schemes were proposed for interconnected nonlinear systems with actuator faults including stuck and loss of effectiveness. However, a common theme of these results in Wang et al. (2009) and Li and Yang (2017) is that the controller is designed without taking into account the disturbances. Furthermore, the large-scale systems are characterized by the triangular form in Wang et al. (2009) and Li and Yang (2017), and the control inputs of each subsystem need to use identical channels, which is usually unrealistic in practice. To our knowledge, there is still no result available on decentralized FTC problem of large-scale multi-input multi-output systems with actuator faults, mismatched interconnections and mismatched disturbances. This motivates the present study.

This paper is concerned with the challenging problem of decentralized adaptive FTC for a class of uncertain interconnected systems with disturbances and actuator faults. The main contributions are summarized as follows: (1) Compared with the work in Jiang and Jiang (2012) where matched interconnections were considered and external disturbances were not taken into account, the system considered here contains mismatched interconnections and mismatched disturbances; (2) Different from the results in Veillette et al. (1992) and Yang and Wang (1999) concerning the problem of decentralized disturbance attenuation, cyclic-small-gain technique is introduced to address the unknown and mismatched interconnections; (3) An adaptive control scheme with backstepping method is developed to compensate automatically the actuator faults and the matched parts of disturbances and interconnections; and (4) In contrast to the results in Wang et al. (2009) and Li and Yang (2017), the proposed approach is easy to implement. Only three parameters need to be estimated online for each subsystem in the implementation of the proposed control scheme. Moreover, the control inputs of each subsystem are required to use identical channels in Wang et al. (2009) and Li and Yang (2017), which is restrictive in practical applications.

Notation: For a matrix $S$, ${\lambda }_{min}\left(S\right)$ and ${\lambda }_{max}\left(S\right)$ denote its minimum eigenvalue and maximum eigenvalue, respectively. The notion $S>0$ means that $S$ is a symmetric positive definite matrix. For a square matrix $M$, $He\left(M\right)$ is defined as $He\left(M\right)=M+M^T$. $0_{m\times n}$ and $I_n$ denote, respectively, the zero matrix with $m\times n$ dimensions and the identity matrix with $n\times n$ dimensions, and their subscripts will be omitted for simplicity whenever without causing any confusion. The symbol $\star$ within a matrix represents the symmetric entry.