Research On Optimal Disturbances Rejection Control Approaches For Discrete-Time Systems With Time-Delays

Based on the present situation on the optimal control problem and optimal output tracking control problem of time-delay systems with external disturbances, this thesis studies the approximate optimal disturbance rejection control and optimal output tracking control of time-delay systems with external disturbances by using the successive approximation approach (SAA). The major results are shown as follows:1,The history of the development in optimal control is reviewed firstly. The latest research tendency of optimal control problem for time-delay systems in this field are introduced and the main methods of disturbance disposal are presented.2,A damping control for linear discrete-time systems with state and input delays affected by sinusoidal disturbances is considered. Firstly, the original system is transformed into a form without input delays through a variable substitution. Then by using the successive approximation approach, the optimal control problem is transformed into a sequence of linear two-point boundary value problems. The optimal control law consists of analytic state feedback, feedforward, and control with memory terms, and a limit term of a sequence of time-delay compensation vectors. By taking the finite-step iteration of the compensation sequence, we can obtain a suboptimal damping control law. Simulations show that the algorithm presented is easily realizable and the controller designed has strong ability to reject sinusoidal disturbances.3,Present an approach to approximating the TPBV problem and hence to designing tracking controllers for time-delay discrete-time systems with finite-time horizon quadratic performance index. To reject sinusoidal disturbances without steady error, we designed a disturbance compensator and the original system is transformed into an augmented system. An iterative process is proposed to find a solution sequence of the TPBV problem with both delay and advance terms, which is obtained from the necessary optimality conditions. The OOTC law consists of analytical state feedback terms and a compensation term, which is the limit of the adjoint vector sequence, which are derived by using the SAA. The result is an iterative scheme, which successively improves the initial control law ultimately converging to the OOTC law. For the same system, the more iteration times of the compensation term in state feedback control law, the better the control effect. A numerical example indicates that the algorithm is effective and robust with respect to sinusoidal disturbances.4,The last section summarizes the main work in this paper and prospects the research of optimal disturbance rejection control problem for the discrete-time systems with time-delays in the future.