An equivalence result in linear-quadratic theory

W.A. van den Broek, J.C. Engwerda, J.M. Schumacher

    Research output: Contribution to journalArticleAcademicpeer-review

    6 Citations (Scopus)

    Abstract

    We consider the zero-endpoint infinite-horizon LQ problem. We show that the existence of an optimal policy in the class of feedback controls is a sufficient condition for the existence of a stabilizing solution to the algebraic Riccati equation. This result is shown without assuming positive definiteness of the state weighting matrix. The feedback formulation of the optimization problem is natural in the context of differential games and we provide a characterization of feedback Nash equilibria both in a deterministic and stochastic context.
    Original languageEnglish
    Pages (from-to)355-359
    Number of pages5
    JournalAutomatica
    Volume39
    Issue number2
    DOIs
    Publication statusPublished - Feb 2003

    Keywords

    • LQG theory
    • LQ theory
    • Differential games
    • Algebraic Riccati equations

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