Pontryagin Optimal Control via Neural Networks

Solving real-world optimal control problems are challenging tasks, as the complex, high-dimensional system dynamics are usually unrevealed to the decision maker. It is thus hard to find the optimal control actions numerically. To deal with such modeling and computation challenges, in this paper, we integrate Neural Networks with the Pontryagin's Maximum Principle (PMP), and propose a sample efficient framework NN-PMP-Gradient. The resulting controller can be implemented for systems with unknown and complex dynamics. By taking an iterative approach, the proposed framework not only utilizes the accurate surrogate models parameterized by neural networks, it also efficiently recovers the optimality conditions along with the optimal action sequences via PMP conditions. Numerical simulations on Linear Quadratic Regulator, energy arbitrage of grid-connected lossy battery, control of single pendulum, and two MuJoCo locomotion tasks demonstrate our proposed NN-PMP-Gradient is a general and versatile computation tool for finding optimal solutions. And compared with the widely applied model-free and model-based reinforcement learning (RL) algorithms, our NN-PMP-Gradient achieves higher sample-efficiency and performance in terms of control objectives.