Hamilton-Jacobi Equations for Two Classes of State-Constrained Zero-Sum Games
Abstract
This paper presents Hamilton-Jacobi (HJ) formulations for two classes of two-player zero-sum games: one with a maximum cost value over time, and one with a minimum cost value over time. In the zero-sum game setting, player A minimizes the given cost while satisfying state constraints, and player B wants to prevent player A's success. For each class of problems, this paper presents two HJ equations: one for time-varying dynamics, cost, and state constraint; the other for time-invariant dynamics, cost, and state constraint. Utilizing the HJ equations, the optimal control for each player is analyzed, and a numerical algorithm is presented to compute the solution to the HJ equations. A two-dimensional water system is introduced as an example to demonstrate the proposed HJ framework.
Cite
@article{arxiv.2106.15006,
title = {Hamilton-Jacobi Equations for Two Classes of State-Constrained Zero-Sum Games},
author = {Donggun Lee and Claire J. Tomlin},
journal= {arXiv preprint arXiv:2106.15006},
year = {2021}
}