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<p>In this paper, we study infinite-horizon deterministic linear-quadratic differential games with state and output feedback information structure. We assume linear time-invariant dynamics and quadratic cost functionals defined over an infinite horizon. We show that the conditions for the existence of an output feedback Nash equilibrium (FNE), available in the literature, are overly stringent, even for low-dimensional games. To address this issue, we introduce the concept of a feedback guaranteed cost equilibrium (FGCE) using ideas from suboptimal control. At an FGCE, the players’ costs are upper-bounded by a specified cost profile while satisfying an equilibrium property. We derive several properties of FGCE. Specifically, we show that FGCE strategies form a broader class of equilibrium strategies: whenever an FNE exists, it is also an FGCE. Furthermore, we demonstrate that sufficient conditions for the existence of an FGCE are related to the solvability of a set of coupled bilinear matrix inequalities. We propose linear matrix inequality-based iterative algorithms for synthesizing FGCE strategies. Finally, we illustrate the performance of FGCE controllers through numerical examples.</p>

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Guaranteed Cost Equilibrium in Infinite-Horizon Deterministic Linear-Quadratic Differential Games

  • 期刊论文

  • 发表日期：

    2025年6月19日

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  • Aniruddha Roy,
  • Puduru Viswanadha Reddy

摘要

In this paper, we study infinite-horizon deterministic linear-quadratic differential games with state and output feedback information structure. We assume linear time-invariant dynamics and quadratic cost functionals defined over an infinite horizon. We show that the conditions for the existence of an output feedback Nash equilibrium (FNE), available in the literature, are overly stringent, even for low-dimensional games. To address this issue, we introduce the concept of a feedback guaranteed cost equilibrium (FGCE) using ideas from suboptimal control. At an FGCE, the players’ costs are upper-bounded by a specified cost profile while satisfying an equilibrium property. We derive several properties of FGCE. Specifically, we show that FGCE strategies form a broader class of equilibrium strategies: whenever an FNE exists, it is also an FGCE. Furthermore, we demonstrate that sufficient conditions for the existence of an FGCE are related to the solvability of a set of coupled bilinear matrix inequalities. We propose linear matrix inequality-based iterative algorithms for synthesizing FGCE strategies. Finally, we illustrate the performance of FGCE controllers through numerical examples.