Linear quadratic zero‐sum game for time‐delayed uncertain stochastic systems

Abstract

SummaryThis study focuses on the analysis of a linear quadratic zero‐sum game (LQZSG) for time‐delayed uncertain stochastic systems. To begin, we introduce a general time‐delayed zero‐sum game. Employing an algebraic transformation method, we transform the time‐delayed zero‐sum game into an equivalent uncertain random zero‐sum game without time delay. Subsequently, we present equilibrium equations that streamline the transformation of the uncertain random zero‐sum game into problems solvable as deterministic difference equations. We then investigate the LQZSG involving a linear time‐delayed uncertain stochastic system with a quadratic objective function. Within this framework, we provide a unified framework for solving this type of game and obtaining the analytic expression for the saddle‐point equilibrium of the LQZSG. Additionally, we present a numerical example and a counter‐terrorism economic game to illustrate the applicability of our findings.