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Pontryagin Neural Networks with Functional Interpolation for Optimal Intercept Problems

Author

Listed:
  • Andrea D’Ambrosio

    (School of Aerospace Engineering, Sapienza University of Rome, 00138 Rome, Italy
    System & Industrial Engineering, University of Arizona, Tucson, AZ 85721, USA)

  • Enrico Schiassi

    (System & Industrial Engineering, University of Arizona, Tucson, AZ 85721, USA)

  • Fabio Curti

    (School of Aerospace Engineering, Sapienza University of Rome, 00138 Rome, Italy)

  • Roberto Furfaro

    (System & Industrial Engineering, University of Arizona, Tucson, AZ 85721, USA
    Aerospace & Mechanical Engineering, University of Arizona, Tucson, AZ 85721, USA)

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.

Suggested Citation

  • Andrea D’Ambrosio & Enrico Schiassi & Fabio Curti & Roberto Furfaro, 2021. "Pontryagin Neural Networks with Functional Interpolation for Optimal Intercept Problems," Mathematics, MDPI, vol. 9(9), pages 1-23, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:9:p:996-:d:545093
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    Cited by:

    1. Yassopoulos, Christopher & Reddy, J.N. & Mortari, Daniele, 2023. "Analysis of nonlinear Timoshenko–Ehrenfest beam problems with von Kármán nonlinearity using the Theory of Functional Connections," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 709-744.

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