State constrained stochastic optimal control for continuous and hybrid dynamical systems using DFBSDE

We develop a computationally efficient learning-based forward–backward stochastic differential equations (FBSDE) controller for both continuous and hybrid dynamical (HD) systems subject to noise state constraints. Solutions optimal control (SOC) problems satisfy the Hamilton–Jacobi–Bellman (HJB) equation. Using current FBSDE-based solutions, can be obtained from HJB using deep neural networks (e.g., long short-term memory (LSTM) networks). To ensure learned respects constraint boundaries, we enforce constraints soft penalty function. In addition previous works, adapt FBSDE (DFBSDE) framework handle HD consisting of dynamics deterministic discrete change. demonstrate our proposed algorithm in simulation on nonlinear system (cart–pole) (five-link biped).