Robust dynamic programming via multi-parametric programming

Abstract In this work; we present a new algorithm for solving complex multi-stage optimisation problems involving hard constraints and uncertainties; based on dynamic and multi-parametric programming. Each echelon of the dynamic programming procedure; typically employed in the context of multi-stage optimisation models; is interpreted as a robust multi-parametric optimisation problem; with the present states and future decision variables being the parameters; while the present decisions the corresponding optimisation variables. This reformulation significantly reduces the dimension of the original problem; essentially to a set of lower dimensional multi-parametric programs; which are sequentially solved. Furthermore; the use of sensitivity analysis circumvents non-convexities that naturally arise in constrained dynamic programming problems. The application of the proposed novel framework to robust constrained optimal control is highlighted.