Risk-Minimizing Two-Player Zero-Sum Stochastic Differential Game via Path Integral Control
- Resource Type
- Conference
- Authors
- Patil, Apurva; Zhou, Yujing; Fridovich-Keil, David; Tanaka, Takashi
- Source
- 2023 62nd IEEE Conference on Decision and Control (CDC) Decision and Control (CDC), 2023 62nd IEEE Conference on. :3095-3101 Dec, 2023
- Subject
- Computing and Processing
Power, Energy and Industry Applications
Robotics and Control Systems
Training
Sufficient conditions
Monte Carlo methods
Stochastic processes
Games
Differential games
Cost function
- Language
- ISSN
- 2576-2370
This paper addresses a continuous-time risk-minimizing two-player zero-sum stochastic differential game (SDG), in which each player aims to minimize its probability of failure. Failure occurs in the event when the state of the game enters into predefined undesirable domains, and one player's failure is the other's success. We derive a sufficient condition for this game to have a saddle-point equilibrium and show that it can be solved via a Hamilton-Jacobi-Isaacs (HJI) partial differential equation (PDE) with a Dirichlet boundary condition. Under certain assumptions on the system dynamics and cost function, we establish the existence and uniqueness of the saddle-point of the game. We provide explicit expressions for the saddle-point policies which can be numerically evaluated using path integral control. This allows us to solve the game online via Monte Carlo sampling of system trajectories. We implement our control synthesis framework on two classes of risk-minimizing zero-sum SDGs: a disturbance attenuation problem and a pursuit-evasion game. Simulation studies are presented to validate the proposed control synthesis framework.