Finite-Horizon Optimal Control Using Neural Networks with an Application to Orbit Transfer Problems
Ali Heydari · 2011
A new controller is developed in this study, called Finite-SNAC, which embeds solutions to the Hamilton-Jacobi-Bellman equations for finite-time problems of control-affine nonlinear systems. This is a single neural network controller and the inputs to the network are the state vector along with the time-to-go and the output is the optimal costate vector to be used in calculating the optimal control vector. Convergence of the reinforcement learning based iterative method to the optimal solution along with the convergence of the training error and the network’s weights are proved. A fixed final time orbital spacecraft maneuver problem is solved and the results show the excellent potential of the proposed technique. A byproduct of the solution process is that the same network can be used to produce optimal feedback control over a range of initial conditions and final times.