含输入和输出时滞离散时间系统的最优跟踪控制

Optimal Output Tracking Control for Discrete-Time Systems with Input and Output Delays

针对一类含有输入时滞和输出时滞的离散时间系统,给出了一种无时滞转换方法,并给出了此类系统在受扰情况下的最优跟踪控制律。为避免求解含有超前项和时滞项的两点边值问题,对原时滞系统进行了无时滞转换。根据系统的最优控制理论,构造了转换后系统的二次性能指标。通过求解Riccati差分方程得到了最优跟踪控制律。构造了扰动外系统观测器和参考输入外系统观测器来解决最优跟踪控制律中所含有的前馈项的物理不可实现问题。仿真实例表明所提出的最优跟踪控制律有效。

In this paper,a non-delay transformation method and an optimal tracking output control(OOTC)law are presented for a class of discrete linear time-invariable systems with input and output delays affected by disturbance.In order to avoid the two-point boundary value problem with items of time-delay and time-advance,the discrete-time system with input and output delays is transformed into a delay-free system.According to the Optimal Control theory for discrete time systems,we give the quadratic performance index without the explicit appearance of time-delay items.An OOTC law is derived from Riccati difference equations.Two observers are proposed to estimate the states of the reference input and the disturbances in order to solve physically unrealizable problem of the OOTC law.Simulation results demonstrate the effectiveness of the optimal output tracking control law.