In this paper, a class of optimal space guidance control problems is solved using the combination of indirect method and Physics-Informed Neural Networks (PINNs). More specifically, we consider the class of optimal control problems with integral quadratic cost. The boundary value problems that arise from the application of the Pontryagin Minimum/Maximum Principle are solved via PINNs, which are particular neural networks where the training of the network is driven by the physics of the problem, modeled through Differential Equations. Three different PINN frameworks are considered, the standard PINN, the Physics-Informed Extreme Learning Machine (PIELM), and Physics-Informed Extreme Theory of Functional Connections (X-TFC). The main difference between standard PINN and PIELM with X-TFC is that with X-TFC initial and boundary conditions are analytically satisfied thanks to the so-called Constrained Expressions, introduced with the original Theory of Functional Connections (TFC). These expressions are a sum of a free-function, expanded as a single layer neural network trained via Extreme Learning Machine (ELM) algorithm, and a functional that analytically satisfies the boundary constraints. The results of this paper show the convenience of employing PINN frameworks to tackle this class of optimal control problems, especially PIELM and X-TFC, as they provide very good accuracy with low computational times.

CLASS OF OPTIMAL SPACE GUIDANCE PROBLEMS SOLVED VIA INDIRECT METHODS AND PHYSICS-INFORMED NEURAL NETWORKS / Schiassi, E.; D’Ambrosio, Andrea; Scorsoglio, A.; Furfaro, R.; Curti, Fabio. - (2021). ((Intervento presentato al convegno 31st AAS/AIAA Space Flight Mechanics Meeting tenutosi a Virtual.

CLASS OF OPTIMAL SPACE GUIDANCE PROBLEMS SOLVED VIA INDIRECT METHODS AND PHYSICS-INFORMED NEURAL NETWORKS

D’Ambrosio Andrea;Curti, Fabio
2021

Abstract

In this paper, a class of optimal space guidance control problems is solved using the combination of indirect method and Physics-Informed Neural Networks (PINNs). More specifically, we consider the class of optimal control problems with integral quadratic cost. The boundary value problems that arise from the application of the Pontryagin Minimum/Maximum Principle are solved via PINNs, which are particular neural networks where the training of the network is driven by the physics of the problem, modeled through Differential Equations. Three different PINN frameworks are considered, the standard PINN, the Physics-Informed Extreme Learning Machine (PIELM), and Physics-Informed Extreme Theory of Functional Connections (X-TFC). The main difference between standard PINN and PIELM with X-TFC is that with X-TFC initial and boundary conditions are analytically satisfied thanks to the so-called Constrained Expressions, introduced with the original Theory of Functional Connections (TFC). These expressions are a sum of a free-function, expanded as a single layer neural network trained via Extreme Learning Machine (ELM) algorithm, and a functional that analytically satisfies the boundary constraints. The results of this paper show the convenience of employing PINN frameworks to tackle this class of optimal control problems, especially PIELM and X-TFC, as they provide very good accuracy with low computational times.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1559754
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