Pontryagin neural networks with functional interpolation for optimal intercept problems

Andrea D’ambrosio, Enrico Schiassi, Fabio Curti, Roberto Furfaro

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Article number996
JournalMathematics
Volume9
Issue number9
DOIs
StatePublished - May 1 2021

Keywords

  • Extreme Learning Machine
  • Functional interpola-tion
  • Optimal control
  • Physics-Informed Neural Networks
  • Pontryagin Neural Networks
  • Theory of Functional Connections

ASJC Scopus subject areas

  • Mathematics(all)

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