Rocket Ascent Trajectory Optimization via Physics-Informed Pontryagin Neural Networks

This paper investigates the application of a Physics-Informed Neural Network framework, named Pontryagin Neural Network (PoNN), to solve the rocket ascent optimal control problem, incorporating a constraint on the maximum dynamic pressure. First, PoNN tackles the optimal control problem using the indirect method and Pontryagin’s Minimum Principle. Then, a neural network approximates the state and costate of the Boundary Value Problem (BVP) associated with the necessary optimality conditions. In the proposed methodology, path inequality constraints are integrated directly into the Hamiltonian with Lagrange multipliers. The multipliers are estimated during the optimization process along with the PoNN output weights, ensuring that they meet the complementarity conditions by using the Fischer-Burmeister function, a positive Lipschitz-continuous function that ensures complementarity when it evaluates to zero. This approach addresses several limitations of traditional methods for incorporating path constraints. It eliminates the need for continuation methods, avoids the addition of differential equations and state variables, and does not rely on penalty functions or other approximation techniques. Additionally, it requires no prior knowledge of the structure of constrained arcs. The results demonstrate the effectiveness of the proposed approach in solving the rocket ascent optimal control problem, achieving high accuracy and optimality.