Pareto optimal controller designs in differential games

In this study, Pareto optimality of controllers is investigated from the perspective of a system designer in a differential game. In the game, each player has their own cost function that must be minimized while competing for the control input, characterized by strategies of players. The controller design problem is formulated as a multiobjective optimization problem constrained by linear matrix inequalities. A novel stochastic algorithm using differential evolution mechanisms is proposed to solve the problem so that a set of Pareto optimal strategies can be obtained. In contrast with existing studies on differential games, this paper considers external disturbances involved in the game and a systematic approach to searching for Pareto optimal solutions.