含有状态时滞的受扰线性离散系统前馈-反馈最优控制

对在随机噪声环境下含状态时滞的线性离散系统的最优控制问题进行了研究。利用卡尔曼滤波算法求得随机干扰的最优估计值,并构造一个敏感度函数,根据麦克劳林展开式将原系统的求取过程转化为通过构造一个两点边值问题族来求解。同时在最优控制律中构造一个补偿函数以减小运算中所带来的误差。将原系统的最优控制律近似估算成M阶前馈-反馈次优控制律,再由分离原理得到含有状态时滞的受扰线性离散系统前馈-反馈最优控制律,最后通过给定一个M的具体值得到M阶的前馈-反馈次优控制律的仿真图像来对比前馈-反馈与经典状态反馈的控制作用,表明前馈-反馈在最优控制律中具有更好的控制效果。

Feedforward-feed Optimum Control of Disturbed Linear Discrete System Including State Time-delay

This paper researches the optimum control problem of linear discrete system including state time-delay in the environment of random noise.Utilize the Kalman filter algorithm to obtain the optimal estimate value of random disturbance and establish a sensitivity function,transform the calculating process of original system into calculating by establish a two-point boundary value problem sequence according to Maclaurin expansion.At the same time,establish a penalty function in the optimal control law to reduce the error generated by calculation.Approximate estimate the optimal control law of original system into M-order feedforward-feed sub-optimal control law.Then separate the feedforward-feed optimum control law of disturbed linear discrete system including state time-delay obtained by principle.At last,obtain the emulational image of M-order feedforward-feed sub-optimal control law by giving a concrete value to M,compare the control effect of feedforward-feed and classic state feed,it indicates that the feedforward-feed has better control effect in the optimum control law.