Value Approximation for Two-Player General-Sum Differential Games with State Constraints

arXiv:2311.16520v2 Announce Type: replace-cross
Abstract: Solving Hamilton-Jacobi-Isaacs (HJI) PDEs numerically enables equilibrial feedback control in two-player differential games, yet faces the curse of dimensionality (CoD). While physics-informed neural networks (PINNs) have shown promise in alleviating CoD in solving PDEs, vanilla PINNs fall short in learning discontinuous solutions due to their sampling nature, leading to poor safety performance of the resulting policies when values are discontinuous due to state or temporal logic constraints. In this study, we explore three potential solutions …

abstract approximation arxiv constraints control cs.gt cs.lg cs.ro differential dimensionality feedback games general hamilton networks neural networks physics physics-informed solutions state sum the curse of dimensionality type value