Asymptotic ε-Nash Equilibrium for 2nd Order Two-Player Nonzero-sum Singular LQ Games with Decentralized Control

Abstract

We propose a new equilibrium concept: asymptotic ε-Nash equilibrium for 2***nd order two-player nonzero-sum games where each player has a control-free cost functional quadratic in the system states over an infinite horizon and each player's control strategy is constrained to be continuous linear state feedback. Based on each player's singular control problem, the asymptotic ε-Nash equilibrium implemented by partial state feedback is constructed and the feedback gains can be found by solving a group of algebraic equations which involves the system coefficients and weighting matrices in the cost functionals. As an illustration of the theories discussed in this paper, a numerical example is given where the partial state feedback gains can be found explicitly in terms of the system coefficients and weighting matrices in the cost functionals.