线性离散时间广义系统的最优预见控制

Optimal preview control of linear discrete-time descriptor systems

本文研究线性离散时间广义系统的最优预见控制器的设计问题.首先完善了关于线性离散时间广义系统最优调节理论的一个定理.然后将一阶前向差分算子作用在状态方程和可预见的目标值信号上,构造了包含可预见目标值信号的广义扩大误差系统,把跟踪问题转化为关于广义扩大误差系统的调节问题,并讨论了广义扩大误差系统的能稳性、因果能控性及因果能观性与原系统相应特性的关系.再利用因果能控性的特点,通过引入预反馈把问题转化为一个等价的广义因果系统的调节问题,对二次型性能指标函数进行改造,将问题转化为从广义扩大误差系统导出的正常系统的最优控制问题.最后利用前述最优调节理论的定理,得到了带有预见前馈补偿的最优预见控制器.为了便于应用,对所得到的理论给出了简明的实现步骤.数值仿真结果说明了理论结果的正确性和有效性.

We studied the design of an optimal preview controller for linear discrete-time descriptor systems. We first improved the theorem on optimal regulator theory for linear discrete-time descriptor systems. Then, we applied the first-order forward difference operator for the status equation and the previewable reference signal. Thus, a descriptor augmented error system with a previewable reference signal was created, and the tracking problem was transformed into a regulator problem of the descriptor augmented error system. We then discussed the relationship between the stability and causal controllability of the transformed and original system. By applying the feature of causal controllability, we introduced pre-feedback to transform the problem into an equivalent regulator problem for the descriptor causal system. The problem was then further transformed into an optimal control problem for a standard system derived from the descriptor augmented error system by modifying the quadratic performance index. Finally, we derived the optimal preview controller with preview action from the theorem thus obtained by improving the optimal regulator theory. For the ease of application, we presented the steps for realizing the theory, and validated the results through numerical simulation.