Optimal Sliding Mode Disturbance Rejection For Systems With Delayed State And Control

Time-delay is a general existence in the practical process of production. The presence of time-delays could seriously degrade performances of the control system, or even drives the system to instability. The sliding mode control (SMC) has a distinguished feature that after reaching the sliding mode, the system has robustness to matched parameter uncertainties and external disturbances, showing great advantage in the process of dealing with time-delay problem and disturbance problem. Therefore, the research of optimal sliding mode disturbance rejection for systems with delayed state and control input is significant both in theory and in practice.For systems with delayed state and control under external persistent disturbances, the problems of optimal sliding surface design, optimal sliding control law and physically realizable problem are considered in this dissertation. The study addresses the following topics and creation:1. The optimal SMC for linear systems with delayed state and control under disturbances is considered. Firstly, for linear systems with delayed state and control, based on a model transformation, the system with delayed state and control is transformed into a system only with state delay. Secondly, by treating some state variables as virtual control, a quadratic performance index is given. An equation about all of the state variables is obtained through the virtual optimal control law, and then we construct a novel optimal sliding surface with this equation. Finally, the optimal SMC problem of the original system with delay terms is transformed into a sequence of linear two-point boundary value (TPBV) problems by using the successive approximation approach (SAA), two iterative sequences of differential equations with known initial and terminal conditions are first constructed, respectively. By the finite-step iteration of the TPBV, approximate solutions for the optimal control are obtained. Sufficient asymptotic stability conditions of the closed-loop systems are derived for linear systems with delayed state and control. 2. The optimal SMC for linear systems with delayed state and control under disturbances is considered. The optimal control technique is employed to construct sliding manifold, so the sliding motion is optimized. State variables with delay and disturbances of the given system are regarded as external disturbances. The conditions of robustness to external disturbances are discussed. The disturbance rejection to solve the physically realizable problem of the optimal sliding motion is analyzed. Then a new SMC is obtained, which drives the trajectories to reach the sliding surface in finite time. The stability of the sliding mode is proved.