动态时滞系统的最优控制

LQ Regulator of Systems with State and Control Timedelay

针对同时存在状态时滞和控制输入时滞的状态空间模型的线性系统和一个积分二次型成本函数,研究了其最优控制问题.采用Lyapunov稳定性定理,导出了闭环系统二次稳定和保证成本函数极小值的LQ(linearquadratic)控制器存在的一个充分条件.为该类系统的LQ控制器设计提供了一种理论方法.

For a class of linear systems with time-delay in Both states and inputs and to the linear quadratic （LQ）cost functional, the problem of designing an optimal controller via memoryless fecdback is studied. A sufficient condition based on Lyapunov stability theorem, which guarantees that the resulting closed loop system is asymptotically stable is derived. Furthermore, it is shown that the feedback controller constructed is a LQ optimality regulator for some cost functional. A design method of LQ controller is provided for the systems given in theory.