Ferramentas para programação dinâmica em malha aberta

Abstract

The dynamic programming technique consists in the decomposition of the dynamic optimization problem in a sequence of sub-problems, obtaining the solution in a swelling way, based on the Bellman's Optimality Principle. However, its numerical solution is prohibitive in a large extent of the practical applications, as it happens in enumerative algorithms. In view of that, suboptimal procedures have been proposed, such as the open-loop methods. In this way, this thesis proposes computationally tractable tools for dynamic programming problems, considering the dynamics in open-loop by the iteration of closed sets throughout the system, similar to the predictive control. We consider problems with discrete-time control actions, with dynamic systems having deterministic or stochastic and linear or nonlinear functions in the mono and multiobjective cases. The impulsive case is solved as a discrete-time dynamic optimization problem, and in the stochastic case, the stochastic dominance concept is used in a multi-quantile approach. Five case studies are presented, showing the application of the proposed methodology in same relevant real-world problems. They are: the optimization of a herd cattle implantation, the optimal distribution network design of electrical energy, the biological control of plagues, the optimal vaccination strategies design, and the stock control. The found solutions are optimal for deterministic problems and sub-optimal for the stochastic ones. The results came from the case studies are satisfactory under the computational and the practical point of view.