Roubst Adaptive Sliding Mode Controller Design For Uncertain Nonlinear Discrete-Time Systems

When considering the actual project,we can not ignore the adverse effects of nonlinear control system.Sliding mode control(SMC)has many advantages,such as strong robustness,anti-interference,insensitive to matched uncertainties,these advantages make the SMC problem in the uncertain nonlinear system more simple,and the control effect is better.However,when SMC theory combined with practical engineering,the SMC will be accompanied by a high gain,chattering,depending on mathematical modeling,uncertainties must satisfy matched conditions and need to be known before.When adaptive control(AC)is applying to uncertain nonlinear system,we can ignore unmodeled dynamics,parameter change and external disturbance,such as insensitive,uncertainties needn't to be known and also don't have to meet the related matching conditions.When the system's own structural parameters change,alternating initial conditions or change the extreme point of the objective function,it can still be automatically maintained in the optimal working state.When the system exists other uncertainties except parameters uncertainties,AC will be influenced by model error,so it can be combined with other robust control technique.Accordingly,to study the discrete uncertain systems,this paper considered the AC and SMC at the same time,an adaptive sliding mode controller was proposed,which is a expansion of currently research.First,the research background and general situation of the robust adaptive sliding mode control for discrete-time uncertain systems was introduced,in the meanwhile,the main contribution and structure arrangement of this paper is presented.Second,the basic theories related to the study of this paper was investigated,such as SMC and AC.Finally,the main research methods and techniques used in this paper are introduced: Lyapunov stability theory and LMI technology.Then,the state feedback method to study the stability analysis and robust adaptive sliding mode control for discrete nonlinear systems with uncertainties was developed.The Lyapunov stability theory and LMI method are used to design the linear sliding surface.According to the characteristics of the sliding surface,an adaptive method is presented to design the sliding mode controller which can ensure the system is asymptotically stable.At last,discrete-time uncertain systems with nonlinearity was studied.The reduced-order system be achieved via singular-value decomposition.Based on the output feedback,the sliding mode surface and the controller are designed to analyze the stability and reachability.Finally,an simulation example is presented to prove the effectiveness of the designed controller.