| 连续时间无穷维正则状态信号系统的最优控制 |
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| 引用本文： | 张倩,刘浏,卢玉峰. 连续时间无穷维正则状态信号系统的最优控制[J]. 控制理论与应用, 2019, 36(10): 1738-1744 |
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| 作者姓名： | 张倩 刘浏 卢玉峰 |
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| 作者单位： | 大连理工大学数学科学学院,辽宁大连,116024 |
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| 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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| 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.
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| 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 |
Optimal control on infinite-dimensional continuous-time regular state signal systems |
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| ZHANG Qian,LIU Liu and LU Yu-feng. Optimal control on infinite-dimensional continuous-time regular state signal systems[J]. Control Theory & Applications, 2019, 36(10): 1738-1744 |
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| Authors: | ZHANG Qian LIU Liu LU Yu-feng |
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| Affiliation: | Dalian University of Technology,Dalian University of Technology and Dalian University of Technology |
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| Abstract: | This paper considers the linear quadratic regulator (LQR) optimal control problem and Kalman filteringproblem for a regular state signal (s/s) system. The solvability of the optimal control problems for the regular s/s systemis equivalent to that for some regular i/s/o representation of the regular s/s system. The connection on optimal future costsbetween the regular s/s system and some regular i/s/o representation with a nonempty resolvent set is proposed. Twoexamples are given to illustrate the results. |
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| Keywords: | regular s/s system regular i/s/o representation LQR optimal control problem Kalman filtering problem generalized stable trajectory |
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