Robust dynamic programming via multi-parametric programming
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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. 2007 Elsevier B.V. All rights reserved.
