Inverse open-loop noncooperative differential games and inverse optimal control

We consider the problem of computing parameters of player cost functionals such that given state and control trajectories constitute an open-loop Nash equilibrium for a noncooperative differential game. We propose two methods for solving this inverse differential game problem and novel conditions under which our methods compute unique cost-functional parameters. Our conditions are analogous to persistence of excitation conditions in adaptive control and parameter estimation. The efficacy of our methods is illustrated in simulations.