Adaptive Fuzzy Backstepping Control For Nonlinear Uncertain Switched Systems

Under the framework of adaptive fuzzy backstepping control, fuzzy logic systems, mutiple Lyapunov function stability theory, common Lyapunov function stability theory, average dwell time method, etc. Systemtically studied the controller design and stability analysis problem for several classes’ uncertain nonlinear switched systems in this thesis. Some adaptive fuzzy output tracking control approaches is proposed, and the stability of the closed-loop system is proved. The detail contents of this thesis are stated as follows:(1) For a class of uncertain nonlinear switched systems with unknown dead-zone and under arbitrary switchings, the fuzzy logic systems are utilized to approximate the unknown switched nonlinear functions. Under the framwork of adaptive fuzzy backstepping control design principle and common Lyapunov function stability theory, an adaptive fuzzy state feedback controller is developed. It is also proved that the proposed control approach can guarantee the stability of the closed-loop system. A numerical simulation example is provided to illustrate the effectiveness of the proposed approach.(2) For a class of nonlinear switched systems with actuator fault and under arbitrary switchings, fuzzy logic systems are used to model the uncertain switched nonlinear systems. Based on the matching conditions, the adaptive fuzzy backstepping contol design principle and common Lyapunov function stability theory, an adaptive fuzzy fault-tolerant control approach is developed. It is also proved that the proposed control approach can guarantee the stability of the closed-loop system. The effectiveness of the proposed approach is illustrated by two simulation examples(a numerical example and an application example).(3) For a class of multiple-input and multiple-output uncertain switched nonlinear systems with unknown control directions and under arbitrary switchings, the fuzzy logic systems are used to identify the unknown switched nonlinear systems. Under the framework of the backstepping control design and common Lyapunov function stability theory, a new adaptive fuzzy output tracking control method is developed. It is also proved that the proposed control approach can guarantee the stability of the closed-loop system. A numerical simulation example is provided to illustrate the effectiveness of the proposed approach.(4)For a class of uncertain nonlinear switched systems with unmeasured states, unmodeled dynamics, and dynamical disturbances. The fuzzy logic systems are used to approximate the unknown switched nonlinear functions and a switched fuzzy state observer is designed for estimating the unmeasured states. Under the framework of adaptive fuzzy backstepping control design, and an adaptive fuzzy output-feedback tracking control approach is developed. Combine multiple Lyapunov function stability theory with average dwell time method, the switching signals is designed to guarrentee the stability of the closed-loop system.The effectiveness of the proposed approach is illustrated by a numerical example.(5) For a class of switched nonlinear systems with unmeasured states, the fuzzy logic systems are used to model the uncertain switched nonlinear systems, and a fuzzy switched state observer is designed to estimate the immeasurable states. In order to overcome the“explosion of complexity” occurs in the classical backstepping design techniques, a command filter is introduced into the backstepping design algorithm, and a command filter-based adaptive fuzzy backstepping output feedback control scheme is developed. The stability of the closed-loop system is proved via average dwell time and multiple Lyapunov function. The effectiveness of the proposed approach is illustrated by a numerical example.