Optimal control of continuous-time system based on differential equation controller

The learning-based differential equation controller (DEC) with high computational efficiency is developed for continuous dynamical systems under noise and state constraints. The solution of the optimal control (OC) problem satisfies the Hamilton-Jacobi-Bellman (HJB) equation. Using existing DEC-based solutions, deep neural networks can be used to obtain optimal control from the HJB equation. To ensure that the learned controller respects the constraint boundary, we use a soft penalty function to enforce the state constraint. A deep DEC control framework is used to deal with a dynamic system consisting of continuous dynamics and state changes.