2023/05/18 by Amartya Mukherjee, Jun Liu, Mukherjee, Amartya +1 · 1 citation
Computer Science · Physics and Astronomy · #Adaptive Dynamic Programming Control #Analysis of PDEs (math.AP) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2305.10952
openalex publication_date 2023/05/18 · openalex created_date 2023/05/21 · openalex updated_date 2026/07/28
This paper proposes an actor-critic algorithm for controlling the temperature of a battery pack using a cooling fluid. This is modeled by a coupled 1D partial differential equation (PDE) with a controlled advection term that determines the speed of the cooling fluid. The Hamilton-Jacobi-Bellman (HJB) equation is a PDE that evaluates the optimality of the value function and determines an optimal controller. We propose an algorithm that treats the value network as a Physics-Informed Neural Network (PINN) to solve for the continuous-time HJB equation rather than a discrete-time Bellman optimality equation, and we derive an optimal controller for the environment that we exploit to achieve optimal control. Our experiments show that a hybrid-policy method that updates the value network using the HJB equation and updates the policy network identically to PPO achieves the best results in the control of this PDE system.