连续时间无穷维正则状态信号系统的最优控制
Optimal control on infinite-dimensional continuous-time regular state signal systems

本文研究连续时间线性无穷维正则状态信号(s/s)系统的最优问题–—线性二次调节器(LQR)最优控制问题和卡 尔曼滤波问题. 正则s/s系统的最优问题可解与正则s/s系统的某个正则i/s/o表示的最优问题可解是等价的. 在正则s/s系 统有一个预解集非空的正则i/s/o表示的前提下, 建立了系统本身的未来最优花费与系统表示的未来最优花费之间的联 系, 并给出了相应的例子.
This paper considers the linear quadratic regulator (LQR) optimal control problem and Kalman filtering problem for a regular state signal (s/s) system. The solvability of the optimal control problems for the regular s/s system is equivalent to that for some regular i/s/o representation of the regular s/s system. The connection on optimal future costs between the regular s/s system and some regular i/s/o representation with a nonempty resolvent set is proposed. Two examples are given to illustrate the results