A multi-parametric programming approach for constrained dynamic programming problems
- 288 Downloads
In this work, we present a new algorithm for solving complex multi-stage optimization problems involving hard constraints and uncertainties, based on dynamic and multi-parametric programming techniques. Each echelon of the dynamic programming procedure, typically employed in the context of multi-stage optimization models, is interpreted as a multi-parametric optimization problem, with the present states and future decision variables being the parameters, while the present decisions the corresponding optimization 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 potential application of the proposed novel framework to robust constrained optimal control is highlighted.
KeywordsDynamic programming Constrained multi-stage models Parametric programming
Unable to display preview. Download preview PDF.
- 1.Apt Krzysztof R. (2003). Principles of Constraint Programming. Cambridge University Press, Cambridge Google Scholar
- 14.Kouramas, K.I., Faísca, N.P., Rustem, B., Pistikopoulos, E.N.: Design of robust parametric controllers for constrained multi-stage optimization problems (to be submitted to Automatica) (2007)Google Scholar
- 17.Pistikopoulos E.N., Georgiadis M.C. and Dua V. (2006). Multi-parametric programming: theory, algorithms, and applications, vol. 1. Wiley-VCH, Weinheim Google Scholar
- 19.Rawlings, J.B.: Tutorial: model predictive control technology. In: Proceedings of the American Control Conference, pp. 662–676. San Diego, USA (1999)Google Scholar