2021/06/28 by Donggun Lee, Claire J. Tomlin, Lee, Donggun +1
Engineering · #Advanced Control Systems Optimization #Computational Fluid Dynamics and Aerodynamics #FOS: Electrical engineering #FOS: Mathematics #Guidance and Control Systems #Optimization and Control (math.OC) #Systems and Control (eess.SY) #Water resources management and optimization #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2106.15006
openalex publication_date 2021/06/28 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
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.