Optimal Modified Feedback Strategies in LQ Games under Control Imperfections
Journal:
arXiv
Published Date:
Mar 24, 2025
Abstract
Game-theoretic approaches and Nash equilibrium have been widely applied
across various engineering domains. However, practical challenges such as
disturbances, delays, and actuator limitations can hinder the precise execution
of Nash equilibrium strategies. This work explores the impact of such
implementation imperfections on game trajectories and players' costs within the
context of a two-player linear quadratic (LQ) nonzero-sum game. Specifically,
we analyze how small deviations by one player affect the state and cost
function of the other player. To address these deviations, we propose an
adjusted control policy that not only mitigates adverse effects optimally but
can also exploit the deviations to enhance performance. Rigorous mathematical
analysis and proofs are presented, demonstrating through a representative
example that the proposed policy modification achieves up to $61\%$ improvement
compared to the unadjusted feedback policy and up to $0.59\%$ compared to the
feedback Nash strategy.
