Inverse Noncooperative Differential Games

Abstract

In this chapter, we generalize and extend the continuous-time inverse optimal control methods and results of Chap. 4 to inverse noncooperative differential games. As in the case of (discrete-time) inverse noncooperative dynamic games considered in Chap. 5, we examine problems involving the computation of parameters in player cost functionals given whole or truncated state and control trajectories that are to constitute open-loop or feedback Nash equilibria. We present methods for solving these inverse problems that exploit either bilevel optimization or conditions for the existence of Nash equilibria derived from continuous-time minimum principles. For problems involving open-loop Nash equilibria, we show that minimum-principle methods reduce to linear or quadratic programs under certain parameterizations of the class of player cost functionals. We also establish conditions under which these open-loop methods yield unique parameters for each player. We highlight the difficulty of pursuing minimum-principle methods of inverse noncooperative differential games for the feedback Nash equilibrium solution concept. Finally, we provide a method and associated uniqueness results for the special case of infinite-horizon linear-quadratic feedback noncooperative differential games. Show more