Guaranteed cost strategies of uncertain LQ closed-loop differential games with multiple players

This paper deals with the problem of designing guaranteed cost state feedback strategies for a class of multiple players nonzero-sum linear quadratic differential games where each player does not know exactly the state equation and model it through a system subject to norm-bounded uncertainties. Sufficient conditions for the existence of the guaranteed cost strategies for uncertain LQ differential games are presented. Furthermore, the problem of designing suboptimal guaranteed cost strategies is considered. A non-convex optimization problem with BMI constrains is formulated to solve a coupled of algebraic Riccati inequalities (ARI) and design the suboptimal guaranteed cost strategies which minimizes the guaranteed cost of the closed-loop LQ differential games and can solve by using LMI Toolbox of MATLAB. An example is given to illustrate the proposed results.