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<p>This paper studies the discrete-time linear-quadratic optimal control problem (LQOCP) for time-delayed descriptor systems in a real Hilbert space, and obtains some novel sufficient conditions for the solvability of the discrete-time LQOCP by the generalized inverse theory and space decomposition technique. Especially, the proposed methods are simpler, easier to verify and compute, and can solve the LQOCP without imposing any range inclusion condition. In addition, our work is verified by some numerical examples.</p>

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Discrete-Time Linear-Quadratic Optimal Control Problems for Time-Delayed Descriptor Systems

  • 期刊论文

  • 发表日期：

    2026年1月28日

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  • Bo Liu,
  • Pengchao Lv,
  • Junjie Huang,
  • Fangcui Jiang,
  • Housheng Su

摘要

This paper studies the discrete-time linear-quadratic optimal control problem (LQOCP) for time-delayed descriptor systems in a real Hilbert space, and obtains some novel sufficient conditions for the solvability of the discrete-time LQOCP by the generalized inverse theory and space decomposition technique. Especially, the proposed methods are simpler, easier to verify and compute, and can solve the LQOCP without imposing any range inclusion condition. In addition, our work is verified by some numerical examples.