Finite-Time Adaptive Fault-Tolerant Control for a Class of Nonlinear Systems with Actuator Faults
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Finite-Time Adaptive Fault-Tolerant Control for a Class of Nonlinear Systems with Actuator Faults Yang Wu1
· Xiqin He1,2 · Libing Wu1
Received: 9 September 2018 / Revised: 1 January 2019 / Accepted: 7 January 2019 © Brazilian Society for Automatics–SBA 2020
Abstract This paper considers the problem of finite-time adaptive fault-tolerant control for a class of nonlinear systems with actuator faults. Based on the strict back-stepping method, the controllers and the corresponding adaptive update laws are designed in each step. Therefore, the effects of actuator faults and unknown parameter uncertainties on the system are effectively compensated. Furthermore, it is shown that tracking errors can converge to a small neighborhood of the origin in a finite-time, and all the closed-loop signals are bounded. Finally, simulation results are given to illustrate the efficiency of the proposed control scheme. Keyword Fault-tolerant control, Adaptive control, Finite-time tracking, Actuator failures, Nonlinear systems.
1 Introduction During the past few years, adaptive fault-tolerant control (AFTC) methods have been developed for various systems. For example, robust adaptive fault-tolerant control problems were studied in Li and Yang (2012), Wang et al. (2016), Wu and Yang (2016) for uncertain linear systems with actuator faults and uncertain nonlinear systems with multiple time delays, respectively. Besides, the method of back-stepping, as a powerful tool, has been also widely used for a great many of systems. For SISO uncertain nonlinear systems, robust back-stepping output tracking control problems were considered in Yu and Zhong (2010) and Wu et al. (2006). Based on mismatched disturbances, composite adaptive disturbance observers were constructed for a class of uncertain nonlinear systems in Sun and Guo (2014) and Sun et al. (2014). In addition, at stated in Chen et al. (2014), for nonlinear delayed systems with unknown dead-zone nonlinearities, an adaptive fuzzy control approach was considered based on fuzzy logic systems (FLSs), and similar to Tong et al. (2014) and Li and
B
Xiqin He [email protected]
1
School of Science, University of Science and Technology Liaoning, Anshan 114051, People’s Republic of China
2
Graduate School, University of Science and Technology Liaoning, Anshan, Liaoning 114051, People’s Republic of China
Yang (2008), fuzzy adaptive actuator failures compensation control problems were investigated for a class of uncertain nonlinear systems. Moreover, for a class of nonlinear systems with unknown control coefficients, the author in Ge and Wang (2002) proposed robust adaptive neural control scheme with the utilization of neural networks (NNs), and the work in Hong et al. (2009) presented a robust adaptive control method based on Nussbaum function, respectively. Because the finite-time method has better convergence performance, it has been largely used for a lot of control systems. (see Zhu et al. (2011), Tan et al. (2016), Huang et al. (2005) and the references therein). Finite-time stability
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