A Computationally Efficient Algorithm for Perturbed Dynamic Programs (A-PDP)

This letter proposes an algorithm for solving perturbed dynamic programs, where first-order corrections are applied to a pre-computed optimal strategy and its corresponding value function using local quadratic approximation. The technique is developed to handle perturbations of external inputs and parameters affecting system dynamics, objective and constraint functions, allowing the application to a wide variety of perturbed problems. The method is applied to the energy optimization of an electric vehicle thermal management system, formulated as a constrained dynamic program where external conditions and target set-point are perturbed from their nominal values. Simulations result show 80% reduction in computation time from a Dynamic Programming (DP) solution, with only minimal effect on the overall controller performance.