Resolução de problemas de controle ótimo algébrico-diferenciais com aplicações em engenharia

Abstract

The Algebraic-Differential Optimal Control Problems (ADOCP), also known as Dynamic Optimization Problems, consist in the determination of control variable profiles that maximize (or minimize) an objective function (measure of performance), subject to algebraic-differential constraints. Mathematically, the complexity observed during the resolution of an algebraicdifferential constraint is can be measured by using the concept of differential index. It is defined as the minimum number of differentiations with respect to time that the algebraic system of equations has to undergo to convert the original system into a set of ordinary differential equations. In this context, the main difficulty associated with the solution of the ADOCP is the fluctuation of the differential index due to the presence of inequality constraints or the linear characteristic of the control variable vector. Traditionally, the numerical solution of the ADOCP has been obtained by using classic optimization techniques (direct methods, indirect techniques, or hybrid approaches). In the last years, due to the success found by approaches that do not make use of information about the gradient of the objective function and constraints in various applications, so called bio-inspired methods have become popular to solve the ADOCP. Among these, we can cite the Water Cycle Algorithm (WCA). This evolutionary approach, proposed by Eskandar et al. (2012), is based on the observation of water cycle process and how rivers and streams flow to the sea in the real world. In this contribution, the WCA is used to solve ADOCP, with applications to mathematical problems and engineering system design, for which the control variable vector was discretized in control elements. A sensitivity analysis of some parameters of the WCA is performed. The results obtained by using the WCA were considered equivalent to those obtained by other evolutionary competing strategies in relation to the final value for the objective function and the number of objective function evaluations required.