Learning Fuel-Optimal Trajectories for Space Applications via Pontryagin Neural Networks

Abstract

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.

DDPG-Based Convex Programming Algorithm for the Midcourse Guidance Trajectory of Interceptor

“…Gaudet et al [22] combine the adaptability of reinforcement learning and the fast learning ability of meta learning, proposing a missile guidance and control method based on reinforcement meta learning. D'Ambrosio et al [23] combine the Pontryagin maximum principle with the powerful learning ability of neural networks to propose a fuel optimal trajectory learning method based on the Pontryagin neural network. However, intelligent optimization algorithms face the problem of falling into local optima.…”