Linear-quadratic optimal control for time-varying descriptor systems via space decompositions

doi:10.19682/j.cnki.1005-8885.2023.1011

中国邮电高校学报(英文) ›› 2023, Vol. 30 ›› Issue (6): 38-48.doi: 10.19682/j.cnki.1005-8885.2023.1011

所属专题：复杂网络传播与网络控制

• Complex Network Identification and Control • 上一篇下一篇

Linear-quadratic optimal control for time-varying descriptor systems via space decompositions

吕鹏超; 黄俊杰; 刘波

1. School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China

2. Ministry of Education Key Laboratory for Intelligent Analysis and Security Governance of Ethnic Languages, Minzu University of China, Beijng 100081, China

收稿日期:2023-05-25 修回日期:2023-10-01 出版日期:2023-12-28 发布日期:2023-12-28
通讯作者: Huang Junjie E-mail:huangjunjie@imu.edu.cn
基金资助:
This work was supported by the National Natural Science Foundation of China ( 11961052, 62173355 ), the Natural

Science Foundation of Inner Mongolia ( 2021MS01006 ), the Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region (NMGIRT2317).

Linear-quadratic optimal control for time-varying descriptor systems via space decompositions

Lv Pengchao, Huang Junjie, Liu Bo

1. School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China

2. Ministry of Education Key Laboratory for Intelligent Analysis and Security Governance of Ethnic Languages, Minzu University of China, Beijng 100081, China

Received:2023-05-25 Revised:2023-10-01 Online:2023-12-28 Published:2023-12-28
Contact: Huang Junjie E-mail:huangjunjie@imu.edu.cn
Supported by:
This work was supported by the National Natural Science Foundation of China ( 11961052, 62173355 ), the Natural

Science Foundation of Inner Mongolia ( 2021MS01006 ), the Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region (NMGIRT2317).

摘要/Abstract

摘要：

This paper aims at solving the linear-quadratic optimal control problems ( LQOCP) for time-varying descriptor systems in a real Hilbert space. By using the Moore-Penrose inverse theory and space decomposition technique, the descriptor system can be rewritten as a new differential-algebraic equation (DAE), and then some novel sufficient conditions for the solvability of LQOCP are obtained. Especially, the methods proposed in this work are simpler and easier to verify and compute, and can solve LQOCP without the range inclusion condition. In addition, some numerical examples are shown to verify the results obtained.

关键词: linear-quadratic optimal control problem (LQOCP), time-varying descriptor system, Moore-Penrose inverse, space decomposition

Abstract: This paper aims at solving the linear-quadratic optimal control problems ( LQOCP) for time-varying descriptor systems in a real Hilbert space. By using the Moore-Penrose inverse theory and space decomposition technique, the descriptor system can be rewritten as a new differential-algebraic equation (DAE), and then some novel sufficient conditions for the solvability of LQOCP are obtained. Especially, the methods proposed in this work are simpler and easier to verify and compute, and can solve LQOCP without the range inclusion condition. In addition, some numerical examples are shown to verify the results obtained.

Key words: linear-quadratic optimal control problem (LQOCP), time-varying descriptor system, Moore-Penrose inverse, space decomposition

Lv Pengchao, Huang Junjie, Liu Bo. Linear-quadratic optimal control for time-varying descriptor systems via space decompositions[J]. The Journal of China Universities of Posts and Telecommunications, 2023, 30(6): 38-48.

Linear-quadratic optimal control for time-varying descriptor systems via space decompositions

Linear-quadratic optimal control for time-varying descriptor systems via space decompositions

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