Robust dynamic programming via multi-parametric programming

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.