Using Neural Networks to Compute Approximate and Guaranteed Feasible Hamilton-Jacobi-Bellman PDE Solutions

Understand

To sidestep the curse of dimensionality when computing solutions to Hamilton-Jacobi-Bellman partial differential equations (HJB PDE), we propose an algorithm that leverages a neural network to approximate the value function.

• We show that our final approximation of the value function generates near optimal controls which are guaranteed to successfully drive the system to a target state.
• Our framework is not dependent on state space discretization, leading to a significant reduction in computation time and space complexity in comparison with dynamic programming-based approaches.
• Using this grid-free approach also enables us to plan over longer time horizons with relatively little additional computation overhead.