Brief paperDecentralized adaptive fault-tolerant control for large-scale systems with external disturbances and actuator faults☆
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 controller design method by using a modified Riccati equation approach. For nonlinear large-scale systems, Yang and Wang (1999) developed a decentralized 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 , and denote its minimum eigenvalue and maximum eigenvalue, respectively. The notion means that is a symmetric positive definite matrix. For a square matrix , is defined as . and denote, respectively, the zero matrix with dimensions and the identity matrix with dimensions, and their subscripts will be omitted for simplicity whenever without causing any confusion. The symbol within a matrix represents the symmetric entry.
Section snippets
System model
Consider a continuous-time large-scale system composed of interconnected subsystems described by where for , , , and are the state, the output of actuator described in (5) , the external disturbance and the output for the th subsystem. . is piecewise continuous in , locally Lipschitz in , and represents the unknown matched
Decentralized adaptive fault-tolerant controller design procedure
We first analyze the stability of the -subsystem (9). The following Lyapunov function candidate is chosen for the -subsystem where with .
In order to derive the relationship between the stabilities of the - and -subsystem in the presence of interconnections, the virtual control law will be designed with the help of cyclic-small-gain technique. Theorem 1 provides a sufficient condition for the existence of such a matrix .
Stability analysis
In this section, the stability of the entire closed-loop system including the large-scale system and decentralized adaptive controller will be established.
Theorem 2 Consider the system (9)–(11), and the decentralized controller (25)with the adaptive laws (29)–(31), (33)– (35). Let Assumptions A1–A4 hold, and the virtual control gain
be determined by Theorem 1. Then, the states of the closed-loop system are uniformly bounded, and the stability of the
-subsystem (9)with disturbance
Simulation studies
Consider a multi-machine power system (Jiang & Jiang, 2012) with governor controllers, where the th generator is controlled by two signals and : where for , . and are the external disturbances. The physical meanings of , , , , , , , , , , can be found in Jiang
Conclusions
In this paper, the decentralized adaptive FTC problem for large-scale systems has been studied. A decentralized FTC scheme with adaptive mechanism and cyclic-small-gain technique has been developed. It has been proved that all signals in the resulting closed-loop system are uniformly bounded and the resulting closed-loop system is asymptotically stable with disturbance attenuation.
Chun-Hua Xie received the B.S. degree in detection, guidance and control technology from North University of China, Taiyuan, China, in 2012, and the M.S. degree in navigation, guidance and control from Northeastern University, Shenyang, China, in 2014. Currently, he is pursuing the Ph.D. degree in control theory and control engineering from Northeastern University, Shenyang, China. His current research interests include adaptive robust control, fault-tolerant control and fault diagnosis.
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Chun-Hua Xie received the B.S. degree in detection, guidance and control technology from North University of China, Taiyuan, China, in 2012, and the M.S. degree in navigation, guidance and control from Northeastern University, Shenyang, China, in 2014. Currently, he is pursuing the Ph.D. degree in control theory and control engineering from Northeastern University, Shenyang, China. His current research interests include adaptive robust control, fault-tolerant control and fault diagnosis.
Guang-Hong Yang received the B.S. and M.S. degrees in mathematics from Northeast University of Technology, China, in 1983 and 1986, respectively, and the Ph.D. degree in control engineering from Northeastern University, China (formerly, Northeast University of Technology), in 1994. He was a Lecturer/Associate Professor with Northeastern University from 1986 to 1995. He joined the Nanyang Technological University in 1996 as a Postdoctoral Fellow. From 2001 to 2005, he was a Research Scientist/Senior Research Scientist with the National University of Singapore. He is currently a Professor at the College of Information Science and Engineering, Northeastern University. His current research interests include fault-tolerant control, fault detection and isolation, nonfragile control systems design, and robust control. Dr. Yang is an Associate Editor for the International Journal of Control, Automation, and Systems (IJCAS), the International Journal of Systems Science (IJSS), the IET Control Theory & Applications, and the IEEE Transactions on Fuzzy Systems.
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This work was supported in part by the Funds of National Natural Science Foundation of China (Grant Nos. 61621004 and 61420106016), and the Research Fund of State Key Laboratory of Synthetical Automation for Process Industries (Grant No. 2013ZCX01). The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Huijun Gao under the direction of Editor Ian R. Petersen.