Resolução de problemas de controle ótimo fracionários aplicados à engenharia

• Ano de defesa: 2022
• Autor(a) principal: Lima, Juliana Veiga Cardoso Fernandes de
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Uberlândia; Brasil; Programa de Pós-graduação em Engenharia Mecânica
• Palavras-chave em Português: Problema de Controle Ótimo; Equação Algébrico-Diferencial Fracionária; Ordem Fracionária; Otimização Mono e Multi-objetivo; Optimal Control Problem; Fractional Order; Mono and Multi-objective Optimization; Fractional Differential Algebraic Equation; CNPQ::ENGENHARIAS::ENGENHARIA MECANICA::MECANICA DOS SOLIDOS; Engenharia mecânica; Teoria dos números algébricos; Engenharia mecânica - Métodos de simulação; Cálculo diferencial
• Link de acesso: https://repositorio.ufu.br/handle/123456789/35488; http://doi.org/10.14393/ufu.te.2022.5025

The study of Optimal Control Problems (OCPs) is an area of great interest and importance in engineering and related areas due to applications that can be developed. In general, the OCP consists of determining the control variable profile that maximizes (or minimizes) an objective function subject to differential-algebraic constraints. Commonly, to solve this type of problem, two classes of approaches can be used, namely, the Direct and the Indirect, as well as it is considered that differential constraints present integer order. In practice, this simplifies the problem analysis, but fails to consider the effect of the fractional order on the obtained profiles. This thesis has as aim goal to solve Fractional Optimal Control Problems (FOCPs). For this purpose, the extension of Orthogonal Collocation Method (OCM) to fractional context to integrate the fractional differential algebraic models is proposed. In this scenario, the following results are presented: i) validation of the proposed simulation technique in mathematical and engineering problems; ii) application of the OCM in an inverse problem using real experimental data; iii) resolution of FOCPs by using the Indirect approach; iv) resolution of a FOCP with specified state variable; and v) resolution of FOCPs by using the Direct approach in mono and multi-objective contexts. For this last class, a new multi-objective optimization strategy is proposed. This consists of association between the Stochastic Fractal Search algorithm and two operators: Pareto’ dominance and crowding distance. The results obtained with the simulation by using the OCM indicate that the proposed numerical methodology configures as an interesting approach for solving fractional differential problems. For the proposed inverse problem, it is observed that the fractional order can be used to increase the quality of fit. From the resolution of FOCPs using Indirect and Direct approaches, it is possible to verify the influence of the fractional order on optimal profiles found. For the FOCP with specified state variable, it is possible to conclude that, depending on the fractional order value, is not possible to find an optimal solution. Finally, for the proposed multi-objective algorithm, it is possible to verify the quality of obtained results in relation to other traditional approach, as well as evaluate the influence of the fractional order on the obtained optimal profiles.