Pontryagin Optimal Controller via Neural Networks

Solving real-world optimal control problems are challenging tasks, as the system dynamics can be highly non-linear or including nonconvex objectives and constraints, while in some cases the dynamics are unknown, making it hard to numerically solve the optimal control actions. To deal with such modeling and computation challenges, in this paper, we integrate Neural Networks with the Pontryagin's Minimum Principle (PMP), and propose a computationally efficient framework NN-PMP. The resulting controller can be implemented for systems with unknown and complex dynamics. It can not only utilize the accurate surrogate models parameterized by neural networks, but also efficiently recover the optimality conditions along with the optimal action sequences via PMP conditions. A toy example on a nonlinear Martian Base operation along with a real-world lossy energy storage arbitrage example demonstrates our proposed NN-PMP is a general and versatile computation tool for finding optimal solutions. Compared with solutions provided by the numerical optimization solver with approximated linear dynamics, NN-PMP achieves more efficient system modeling and higher performance in terms of control objectives.