Pontryagin Neural Networks with Functional Interpolation for Optimal Intercept Problems

Mathematics

Fabio Curti¹  Andrea D'Ambrosio¹  Roberto Furfaro²  Enrico Schiassi² 

[1] School of Aerospace Engineering, Sapienza University of Rome, 00138 Rome, Italy;System & Industrial Engineering, University of Arizona, Tucson, AZ 85721, USA;

关键词: Pontryagin Neural Networks;    Physics-Informed Neural Networks;    functional interpolation;    Theory of Functional Connections;    Extreme Learning Machine;    optimal control;   

DOI  :  10.3390/math9090996

来源: DOAJ

【 摘 要 】

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

【 授权许可】

Unknown