Research On Finite-Time Control And Synchronization Problem For Some Classes Of Nonlinear Systems

In this thesis,we focus on the finite-time control and finite-time synchronization problems for some classes of nonlinear systems.We then present the controller design methods to en-sure the stability of closed-loop systems for discrete nonlinear quadratic systems and discrete nonlinear time-varying systems.Controller design methods are proposed for multiple chaotic systems,complex dynamic networks and coupled neural networks to ensure they are synchro-nized in finite-time.Finally,numerical simulations are given to illustrate the effectiveness of the derived results.The main work of the paper can be summarized as follows:(1)A state feedback controller design method is presented for a nonlinear quadratic sys-tem with actuator saturation,assuming the actuator saturation system phenomenon occurs randomly and the stochastic occurring rate of saturation is unknown and time-varying.More-over,by using the Lyapunov stability theorem and LMI technology,sufficient conditions are obtained to guarantee the finite-time stability of closed-loop system.(2)Controller design methods for discrete time-varying systems with randomly occurring nonlinear perturbations and missing measurements are proposed to ensure the finite-time sta-bility of closed-loop systems.The Bernoulli random variable is used to describe the randomly occurring nonlinear perturbation,and a series of random variables with any discrete probabil-ity distribution over the interval[0,1]is introduced to characterize the missing measurement.Assuming that the missing measurement occurs and the loss rate of measurement is time-varying,while the upper and lower bounds for loss rate of measurement are known,the design methods of state feedback and output feedback controller are presented respectively.Accord-ing to the time-varying characteristics of the system,a recursive control algorithm which is easily executed online is presented,and a criterion to ensure the stability of the closed-loop system is also obtained.(3)Finite-time synchronization control is studied for multiple chaotic systems with dif-ferent structures.By designing an appropriate adaptive law,the controller gain can then be adjusted online.An adaptive finite-time controller design method is presented.In theory,it is proved that the adaptive controller can guarantee the synchronization of multiple different chaotic systems in finite time,and the estimation of the upper bound of setting time is given.(4)Finite-time sliding mode synchronization control of complex dynamic networks cou-pled by multiple subsystems is studied.A non-singular terminal sliding surface is designed to ensure the finite-time stability of the sliding mode dynamic.The corresponding sliding mode controller and adaptive sliding mode controller are designed respectively for the two cases of known coupling weight and unknown coupling weight of complex dynamic networks.Using the Lyapunov stability and finite time stability theorem,the finite time stability of complex network error dynamic systems is proved theoretically and the upper bound of synchronous transition time is estimated.(5)Considering actuator failure,a fault-tolerant control method of finite-time synchro-nization is realized for a class of coupled neural networks.In the event of actuator failure,a fault-tolerant synchronization controller and an adaptive fault-tolerant synchronization con-troller are designed for the known and unknown parameters of each node with neural networks.The actuator failures considered are both deviation failures and actuator part-failures.Then,it is proved that the state trajectory of the coupled neural network and the target neural net-work can be synchronized in a finite time.In order to solve the problem that the synchronous setting time depends on the initial condition of the network,a design method of a fixed-time synchronous fault-tolerant controller is also given,where the synchronous setting time of this method is independent of the initial condition of the network.In the end,the simulation results proves that the designed controller can still guarantee better control performance in the event of network failure.