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

作　　者：LüPengchao Huang Junjie Liu Bo 

机构地区：[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,Beijing 100081,China

出　　处：《The Journal of China Universities of Posts and Telecommunications》2023年第6期38-48,共11页中国邮电高校学报（英文版）

基　　金：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：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 

分 类 号：O232[理学—运筹学与控制论]