The Journal of China Universities of Posts and Telecommunications ›› 2023, Vol. 30 ›› Issue (6): 38-48.doi: 10.19682/j.cnki.1005-8885.2023.1011

Special Issue: 复杂网络传播与网络控制

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

Lv Pengchao, Huang Junjie, Liu Bo   

  1. 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
  • 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).

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