Soft-Constrained Output Feedback Guaranteed Cost Equilibria in Infinite-Horizon Uncertain Linear-Quadratic Differential Games

Aniruddha Roy () and Puduru Viswanadha Reddy ()
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Aniruddha Roy: Indian Institute of Technology–Madras
Puduru Viswanadha Reddy: Indian Institute of Technology–Madras

Journal of Optimization Theory and Applications, 2025, vol. 204, issue 2, No 12, 33 pages

Abstract: Abstract In this paper, we study infinite-horizon linear-quadratic uncertain differential games with an output feedback information structure. We assume linear time-invariant nominal dynamics influenced by deterministic external disturbances, and players’ risk preferences are expressed by a soft-constrained quadratic cost criterion over an infinite horizon. We demonstrate that the conditions available in the literature for the existence of a soft-constrained output feedback Nash equilibrium (SCONE) are too stringent to satisfy, even in low-dimensional games. To address this issue, using ideas from suboptimal control, we introduce the concept of a soft-constrained output feedback guaranteed cost equilibrium (SCOGCE). At an SCOGCE, the players’ worst-case costs are upper-bounded by a specified cost profile while maintaining an equilibrium property. We show that SCOGCE strategies form a larger class of equilibrium strategies; that is, whenever an SCONE exists, it is also an SCOGCE. We demonstrate that sufficient conditions for the existence of SCOGCE are related to the solvability of a set of coupled bi-linear matrix inequalities. Using semi-definite programming relaxations, we provide linear matrix inequality-based iterative algorithms for the synthesis of SCOGCE strategies. Finally, we illustrate the performance of SCOGCE controllers with numerical examples.

Keywords: Dynamic games with uncertainty; Linear quadratic differential games; Output feedback Nash equilibrium; Linear matrix inequality; 91A23; 93A16; 93B36 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-024-02575-3

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