Adaptive Fuzzy Control For Fractional Order Nonlinear Systems

For some classes of fractional order nonlinear systems,by utilizing adaptive backstepping control design techniques,the property of fuzzy logic systems,and fractional Lyapunov stability theory,this thesis studies adaptive fuzzy fault-tolerant control design problems,event-triggered control design problems and the stability analysis of the control systems.The simulation results are carried out to validate the effectiveness of the designed scheme.The major contents of this thesis are as follows:An adaptive fuzzy fault-tolerant control problem is investigated for a class of fractional order non-strict feedback nonlinear systems with actuator faults.First,an adaptive fuzzy fault-tolerant control scheme is proposed on the basis of backstepping techniques,where fuzzy logic systems are used to approximate unknown nonlinear functions.The fuzzy basis function is used to avoid the algebraic loop problem caused by utilizing the traditional control schemes.Second,the bound estimation approach is used to estimate the upper bound of the uncertainty caused by actuator faults.An intermediate controller is designed to compensate for the actuator faults,where the number of them is allowed to be infinite.Finally,the fractional Lyapunov stability theory proved that the tracking error enters into a small region around the origin in finite time and all the signals of the closed-loop system are bounded.The problem of the adaptive fuzzy event-triggered control for a class of strict feedback fractional order nonlinear systems is studied.First,an adaptive fuzzy event-triggered control scheme is proposed on the basis of event-triggering mechanisms and backstepping techniques,which uses fuzzy logic systems to approximate unknown nonlinear functions of the system.The character of the proposed control scheme is that the controller of the fixed threshold mechanism only updates and transmits the signal when the system performance index exceeds a certain threshold,thus further reducing the consumption of system resources.Second,the hyperbolic tangent function is used to compensate for the fixed threshold,so that the closed-loop system does not need to satisfy the input state stability condition.Finally,the stability of the system is proved by fractional Lyapunov stability theory.An adaptive fuzzy event-triggered control scheme is proposed for a class of fractional order nonlinear systems with full-state constraints.First,adaptive fuzzy backstepping techniques,event-triggered control strategies and the barrier Lyapunov functions are combined to develop an adaptive fuzzy event-triggered control scheme on the basis of the relative threshold strategy.The feature of this scheme is that the relative threshold strategy not only reduces the communication volume of the system,the designed threshold changes dynamically with the control signal,which further improves the flexibility of the control scheme.Second,the barrier Lyapunov function is used to ensure that the full-state constraints of the fractional order nonlinear system are not violated.Finally,the semi-globally uniformly ultimately bounded stability is ensured through fractional Lyapunov stability theory.An adaptive fuzzy finite-time event-triggered control is proposed for a class of strict feedback fractional order nonlinear systems.First,backstepping techniques,finite-time control strategies and fuzzy logic systems are combined to develop an adaptive fuzzy finite-time event-triggered control scheme on the basis of the relative threshold strategy.The feature of this scheme is that the constructed relative threshold mechanism not only effectively reduces the update and transmission times of the signals,but also does not satisfy the input state stability condition.Second,combining the fractional Lyapunov stability theory and the finite time stability criteria,it is proved that the tracking error enters into a small region around the origin in finite time and all the signals of the closed-loop system are bounded.Finally,the effectiveness of the proposed scheme is verified by a simulation example.