Sliding Mode Control For Discrete-time Systems Based On Riccati Equation

Nowadays,the complexity of controlled objects in control systems continues to increase,and uncertainties such as unmodeled parts,parameter perturbations,and external disturbances present significant challenges to the reliability,robustness,and control accuracy of control systems.Sliding mode control,as an effective anti-interference method,has received widespread attention in the control community.In addition,with the development of computers,control systems are mostly implemented by digital computers.Therefore,studying the sliding mode control problem of discrete-time systems under uncertainty has more theoretical and practical significance.This thesis focuses on the problems of sliding mode control for discrete-time systems based on Riccati equation,including hyperplane design problem,chattering analysis,mismatched disturbance and consensus problem of multi-agent systems.The main contents and innovations are as follows:(1)The Riccati equation and inequality have been utilized to intuitively design the hyperplane for the sliding mode control.Based on the relationship between the Riccati equation and the Lyapunov stability,the sufficient and necessary conditions of the existing of sliding surface have been given and the inter-relations have been clarified for the fundamental requirement on choosing the hyperplane matrix,the stabilizability assumption,the standard Riccati equation,and the Riccati inequality.(2)A state and disturbance observer is introduced in discrete-time sliding mode control to achieve its applicability when only partial system states can be measured.In order to improve the performance of the system in control updating times,a novel event-triggered discrete-time sliding mode control with a state and disturbance observer is proposed.It is shown that the proposed method achieves quasi sliding mode with a small boundary layer.(3)The observer-based sliding mode control problems have been addressed for discretetime systems with unmatched disturbances.First,a modified sliding surface has been designed by introducing the estimation of the unmatched disturbance.Second,a chattering-free sliding mode controller based on non-smooth control has been utilized.Third,it has been proven that the stability of the closed-loop system is achieved by choosing appropriate hyperplane matrices.The hyperplane design methods are based on the discrete-time Riccati equation and the least squares problem.(4)The discrete-time sliding mode control for leader-following and leaderless synchronizations of discrete-time linear dynamical networks have been established.A novel integral sliding surface is designed by integrating the agents’ own states with the combinational-states and a novel hyperplane design method proposed based on the modified Riccati equation.Under the proposed integral sliding surface,the quasi sliding mode motion is achieved with a small boundary layer and the design of each agent’s control input does not need the information of its neighbours’ control inputs,which avoids the use of the inverse of the Laplacian matrix.The stability of the closed-loop system is analyzed based on Lyapunov function.The inter-relations between the hyperplane design,the Laplacian matrix and the Riccati equation are clarified.