Nash Equilibrium Sequence in a Singular Two-Person Linear-Quadratic Differential Game

A finite-horizon two-person non-zero-sum differential game is considered. The dynamics of the linear. Each players has a quadratic functional on its own disposal, which should be minimized. case where weight matrices in control costs one player are singular both functionals studied. Hence, under consideration singular. novel definition Nash equilibrium this (a sequence) proposed. solved by application regularization method. This method yields new game, regular game. Moreover, partial cheap An asymptotic analysis carried out. Based analysis, sequence pairs players’ state-feedback controls constructed. expressions for optimal values obtained. Illustrative examples presented.