Fault-tolerant Control For A Class Of Uncertain Non-linear Systems With Time-varying Delays

With the rapid development of science and technology,modern control systems are becoming more and more large and complicated.Once an accident occurs in the control system,people's lives and properties will be seriously threatened.Therefore,improving the reliability and security of modern complex control system is an urgent problem to be solved.The theory of fault-tolerant control supplies a new way to solve this problem.The uncertainty and nonlinearity of the system model,time-varying delay and actuator faults are common factors that affect the stability of the system.Therefore,studying the uncertain non-linear systems with time-varying delay and actuator faults will present significant value both in theory and practice.Based on Lyapunov stability theory and linear matrix inequality(LMI),the fault-tolerant control problems of uncertain nonlinear systems with time-varying delay and actuator faults are studied by constructing reasonable Lyapunov-Krasovskii functions.The sufficient conditions of asymptotic stability and the design methods of fault-tolerant controllers are given for the common factors including the uncertainties and nonlinearities of the mathematical model,time-varying delay of the state or input,actuator faults et al.The validity and feasibility of the controllers are verified by the model simulations.The main research contents are as follows:Firstly,Non-fragile fault-tolerant control is studied for the uncertain nonlinear system with actuator faults.The asymptotic stability conditions and controller design methods are given for the cases with or without delays and controller parameter perturbations.Where,the system delay is bounded by a bounded function.Controller parameter perturbations include two forms: additive perturbation and multiplicative perturbation.Secondly,Non-fragile fault-tolerant control problem is studied for the uncertain nonlinear systems with input time-varying delay and state time-varying delay.Memoryless and memory non-fragile state fault-tolerant controller is designed for the case of actuator continuous fault.Where,the parameter perturbation of the controller is the additive perturbation.Finally,Integrated active and passive fault-tolerant control problem is studied for the cases of loss of effectiveness,bias faults,outage,and stuck faults of the actuator.,By combining the advantages of passive fault tolerance and active fault tolerance,a fixed gain controller is designed according to passive fault tolerance theory for the common factors such as time-varying delay,the uncertainties and nonlinearities in the system's mathematical model.At the same time,an adaptive compensation controller is designed for unknown actuator faults.Then,the delay-independent & delay-dependent asymptotic stability conditions and controller design methods of the system are given for the above cases.Where,the delay-dependent stability condition has no limit for the derivative of the delay.According to the free weighting matrix technique,there is no inequality scaling for the processing of the delay cross term.A less conservative processing method is used to deal with the uncertainty of the system,so the conservation of the controller is decreased greatly.