Learning Fuel-Optimal Trajectories for Space Applications via Pontryagin Neural Networks
This paper demonstrates the utilization of Pontryagin Neural Networks (PoNNs) to acquire control strategies for achieving fuel-optimal trajectories. PoNNs, a subtype of Physics-Informed Neural Networks (PINNs), are tailored for solving optimal control problems through indirect methods. Specifically,...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-03-01
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| Series: | Aerospace |
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| Online Access: | https://www.mdpi.com/2226-4310/11/3/228 |
| _version_ | 1797242463829622784 |
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| author | Andrea D’Ambrosio Roberto Furfaro |
| author_facet | Andrea D’Ambrosio Roberto Furfaro |
| author_sort | Andrea D’Ambrosio |
| collection | DOAJ |
| description | This paper demonstrates the utilization of Pontryagin Neural Networks (PoNNs) to acquire control strategies for achieving fuel-optimal trajectories. PoNNs, a subtype of Physics-Informed Neural Networks (PINNs), are tailored for solving optimal control problems through indirect methods. Specifically, PoNNs learn to solve the Two-Point Boundary Value Problem derived from the application of the Pontryagin Minimum Principle to the problem’s Hamiltonian. Within PoNNs, the Extreme Theory of Functional Connections (X-TFC) is leveraged to approximate states and costates using constrained expressions (CEs). These CEs comprise a free function, modeled by a shallow neural network trained via Extreme Learning Machine, and a functional component that consistently satisfies boundary conditions analytically. Addressing discontinuous control, a smoothing technique is employed, substituting the sign function with a hyperbolic tangent function and implementing a continuation procedure on the smoothing parameter. The proposed methodology is applied to scenarios involving fuel-optimal Earth−Mars interplanetary transfers and Mars landing trajectories. Remarkably, PoNNs exhibit convergence to solutions even with randomly initialized parameters, determining the number and timing of control switches without prior information. Additionally, an analytical approximation of the solution allows for optimal control computation at unencountered points during training. Comparative analysis reveals the efficacy of the proposed approach, which rivals state-of-the-art methods such as the shooting technique and the adaptive Gaussian quadrature collocation method. |
| first_indexed | 2024-04-24T18:39:38Z |
| format | Article |
| id | doaj.art-32136de1b4d84e3a88cb482ee0157bcb |
| institution | Directory Open Access Journal |
| issn | 2226-4310 |
| language | English |
| last_indexed | 2024-04-24T18:39:38Z |
| publishDate | 2024-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Aerospace |
| spelling | doaj.art-32136de1b4d84e3a88cb482ee0157bcb2024-03-27T13:15:43ZengMDPI AGAerospace2226-43102024-03-0111322810.3390/aerospace11030228Learning Fuel-Optimal Trajectories for Space Applications via Pontryagin Neural NetworksAndrea D’Ambrosio0Roberto Furfaro1Systems & Industrial Engineering, University of Arizona, Tucson, AZ 85721, USASystems & Industrial Engineering, University of Arizona, Tucson, AZ 85721, USAThis paper demonstrates the utilization of Pontryagin Neural Networks (PoNNs) to acquire control strategies for achieving fuel-optimal trajectories. PoNNs, a subtype of Physics-Informed Neural Networks (PINNs), are tailored for solving optimal control problems through indirect methods. Specifically, PoNNs learn to solve the Two-Point Boundary Value Problem derived from the application of the Pontryagin Minimum Principle to the problem’s Hamiltonian. Within PoNNs, the Extreme Theory of Functional Connections (X-TFC) is leveraged to approximate states and costates using constrained expressions (CEs). These CEs comprise a free function, modeled by a shallow neural network trained via Extreme Learning Machine, and a functional component that consistently satisfies boundary conditions analytically. Addressing discontinuous control, a smoothing technique is employed, substituting the sign function with a hyperbolic tangent function and implementing a continuation procedure on the smoothing parameter. The proposed methodology is applied to scenarios involving fuel-optimal Earth−Mars interplanetary transfers and Mars landing trajectories. Remarkably, PoNNs exhibit convergence to solutions even with randomly initialized parameters, determining the number and timing of control switches without prior information. Additionally, an analytical approximation of the solution allows for optimal control computation at unencountered points during training. Comparative analysis reveals the efficacy of the proposed approach, which rivals state-of-the-art methods such as the shooting technique and the adaptive Gaussian quadrature collocation method.https://www.mdpi.com/2226-4310/11/3/228fuel optimal trajectoriesmachine learningPontryagin Neural NetworksPhysics-Informed Neural NetworksExtreme Theory of Functional Connectionsoptimal control |
| spellingShingle | Andrea D’Ambrosio Roberto Furfaro Learning Fuel-Optimal Trajectories for Space Applications via Pontryagin Neural Networks Aerospace fuel optimal trajectories machine learning Pontryagin Neural Networks Physics-Informed Neural Networks Extreme Theory of Functional Connections optimal control |
| title | Learning Fuel-Optimal Trajectories for Space Applications via Pontryagin Neural Networks |
| title_full | Learning Fuel-Optimal Trajectories for Space Applications via Pontryagin Neural Networks |
| title_fullStr | Learning Fuel-Optimal Trajectories for Space Applications via Pontryagin Neural Networks |
| title_full_unstemmed | Learning Fuel-Optimal Trajectories for Space Applications via Pontryagin Neural Networks |
| title_short | Learning Fuel-Optimal Trajectories for Space Applications via Pontryagin Neural Networks |
| title_sort | learning fuel optimal trajectories for space applications via pontryagin neural networks |
| topic | fuel optimal trajectories machine learning Pontryagin Neural Networks Physics-Informed Neural Networks Extreme Theory of Functional Connections optimal control |
| url | https://www.mdpi.com/2226-4310/11/3/228 |
| work_keys_str_mv | AT andreadambrosio learningfueloptimaltrajectoriesforspaceapplicationsviapontryaginneuralnetworks AT robertofurfaro learningfueloptimaltrajectoriesforspaceapplicationsviapontryaginneuralnetworks |