Physics-Informed Neural Networks for Closed-Loop Guidance and Control in Aerospace Systems

Physics-Informed Neural Networks (PINNs) refer to recently defined a class of machine learning algorithms where the learning process for both regression and classification tasks is constrained to satisfy differential equations derived by the straightforward application of known physical laws. Indeed, Deep Neural Networks have been successfully employed to solve a variety of ODEs and PDEs arising in fluid mechanics, quantum mechanics, just to mention a few. Optimal control problems, i.e. finding a feasible control that minimizes a cost functional while satisfying physical, state and control constraints, are generally difficult to solve and one may need to resort to specialized numerical methods. In this work, we show how PINNs can be employed to synthesize closed-loop optimal guidance and control policies by learning the solution of the Hamilton-Jacobi-Bellman Equation (HJBE) via shallow and deep networks. We show that such methods can be coupled with the Theory of Functional Connections to create numerical frameworks that generate efficient and accurate solutions of the HJBE resulting in novel architectures for closed-loop G&C that may enable autonomy in a large class of aerospace systems.