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研究了一类具有状态时滞的时变离散时间系统的最优预见控制问题.所用的方法仍然是通过引入差分算子构造扩大误差系统.首先克服了差分算子不是线性算子的困难,成功构造了扩大误差系统.然后通过提升技术,把系统转化为形式上没有时滞的普通控制系统.最后通过引入可预见的目标值信号信息,得到最终的扩大误差系统.从这个扩大误差系统出发,利用时变系统最优控制的有关结果,设计处理原系统的带有预见作用的控制器.利用矩阵分解,把需要求解的高阶Riccati方程转化成一个低阶的Riccati方程.仿真实例表明了该设计方法的有效性.
The optimal predictive control problem for a class of time-varying discrete-time systems with state delay is studied. The method used is to construct an augmented error system by introducing differential operators. First, the difficulty of the differential operator that is not a linear operator is overcome. Then the system is transformed into a formal control system with no delay in time by lifting technology.Finally, the final expansion error system is obtained by introducing the predictable signal value of the target value.From this expansion error system, Based on the results of the optimal control of time-varying systems, the controller with the predictive function of the original system is designed and processed, and the high order Riccati equation to be solved is decomposed into a low order Riccati equation by matrix decomposition. The effectiveness of the design method.