TY - JOUR

T1 - Physics-Informed Neural Networks for Optimal Planar Orbit Transfers

AU - Schiassi, Enrico

AU - D’ambrosio, Andrea

AU - Drozd, Kristofer

AU - Curti, Fabio

AU - Furfaro, Roberto

N1 - Publisher Copyright:
© AIAA International. All rights reserved.

PY - 2022

Y1 - 2022

N2 - This paper presents a novel framework, combining the indirect method and Physics-Informed Neural Networks (PINNs), to learn optimal control actions for a series of optimal planar orbit transfer problems. According to the indirect method, the optimal control is retrieved by directly applying the Pontryagin minimum principle, which provides the first-order necessary optimality conditions. The necessary conditions result in a two-point boundary value problem (TPBVP) in the state–costate pair, constituting a system of ordinary differential equations, representing the physics constraints of the problem. More precisely, the goal is to model a neural network (NN) representation of the state–costate pair for which the residuals of the TPVBP are as close to zero as possible. This is done using PINNs, which are particular NNs where the training is driven by the problem’s physics constraints. A particular PINN method will be used, named Extreme Theory of Functional Connections (X-TFC), which is a synergy of the classic PINN and the Theory of Functional Connections. With X-TFC, the TPBVP’s boundary conditions are analytically satisfied. This avoids having unbalanced gradients during the network training. The results show the feasibility of employing PINNs to tackle this class of optimal control problems for space applications.

AB - This paper presents a novel framework, combining the indirect method and Physics-Informed Neural Networks (PINNs), to learn optimal control actions for a series of optimal planar orbit transfer problems. According to the indirect method, the optimal control is retrieved by directly applying the Pontryagin minimum principle, which provides the first-order necessary optimality conditions. The necessary conditions result in a two-point boundary value problem (TPBVP) in the state–costate pair, constituting a system of ordinary differential equations, representing the physics constraints of the problem. More precisely, the goal is to model a neural network (NN) representation of the state–costate pair for which the residuals of the TPVBP are as close to zero as possible. This is done using PINNs, which are particular NNs where the training is driven by the problem’s physics constraints. A particular PINN method will be used, named Extreme Theory of Functional Connections (X-TFC), which is a synergy of the classic PINN and the Theory of Functional Connections. With X-TFC, the TPBVP’s boundary conditions are analytically satisfied. This avoids having unbalanced gradients during the network training. The results show the feasibility of employing PINNs to tackle this class of optimal control problems for space applications.

UR - http://www.scopus.com/inward/record.url?scp=85124038161&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85124038161&partnerID=8YFLogxK

U2 - 10.2514/1.A35138

DO - 10.2514/1.A35138

M3 - Article

AN - SCOPUS:85124038161

VL - 59

SP - 834

EP - 849

JO - Journal of Spacecraft and Rockets

JF - Journal of Spacecraft and Rockets

SN - 0022-4650

IS - 3

ER -