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
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DOI编号  10.7641/CTA.2019.18170
  2019,36(10):1738-1744
中文关键词  正则状态信号(s/s)系统  正则i/s/o表示  线性二次调节器(LQR)最优控制问题  卡尔曼滤波问题  广义稳定轨 迹
英文关键词  regular s/s system  regular i/s/o representation  LQR optimal control problem  Kalman filtering problem  generalized stable trajectory
基金项目  Supported by the National Natural Science Foundation of China (11871131, 11671065) and the Fundamental Research Funds for the Central Universities (DUT18LK17).
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作者单位
张倩 大连理工大学 
刘浏 大连理工大学 
卢玉峰 大连理工大学 
中文摘要
      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.
英文摘要
      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.