Adaptive Fuzzy Fault-Tolerant Control of Fractional-Order Chaotic Systems With Full State Constraints and Actuator Faults
摘要
This paper focuses on adaptive fuzzy fault-tolerant control for fractional-order chaotic systems with full state constraints and actuator faults. Integrating with the backstepping strategy, Fuzzy logic systems are constructed to approximate unknown functions. A fractional filtering strategy, which can obtain the estimations of virtual controllers as well as their fractional derivatives and effectively avoid repeatedly differentiating the fractional-order virtual controllers, is presented. In order to avoid full state violating constraints, a barrier Lyapunov function is constructed in each backstepping step. Specifically, a sufficient and necessary condition is provided to facilitate the stability analysis. An inequality about the fractional derivative of a certain convex function is derived, which can be applied to stability analysis of fractional systems with state constraints. According to fractional-order Lyapunov stability analysis, the proposed controller together with fractional adaptive laws, can ensure that not only system output tracks reference signal, but also all states are bounded and do not violate the full state constraints. Lastly, by using a two-order fractional-order chaotic system as an example, the feasibility of the control strategy is demonstrated.