Pontryagin Neural Networks with Functional Interpolation for Optimal Intercept Problems

In this work, we introduce Pontryagin Neural Networks (PoNNs) and employ them to learn the optimal control actions for unconstrained constrained intercept problems. PoNNs represent a particular family of Physics-Informed (PINNs) specifically designed tackling problems via Minimum Principle (PMP) application (e.g., indirect method). The PMP provides first-order necessary optimality conditions, which result in Two-Point Boundary Value Problem (TPBVP). More precisely, from unknown solutions arising TPBVP, modeling with (NNs). characteristic feature is use PINNs combined functional interpolation technique, named Theory Functional Connections (TFC), forms so-called PINN-TFC based frameworks. According these frameworks, are modeled TFC’s expressions using NNs as free functions. results show that can be successfully applied controls class considered paper.