Controle Extremal para uma Classe de Equações Diferenciais Parciais da Onda com Amortecimento Kelvin-Voigt

Paulo Cesar Souza da Silva; Paulo César Pellanda; Tiago Roux Oliveira; Gustavo Artur de Andrade

doi:10.20906/SBAI-SBSE-2023/3812

Paulo Cesar Souza da Silva Programa de Pós-Graduação em Engenharia de Defesa, Instituto Militar de Engenharia (IME), Rio de Janeiro – RJ
Paulo César Pellanda Programa de Pós-Graduação em Engenharia de Defesa, Instituto Militar de Engenharia (IME), Rio de Janeiro – RJ
Tiago Roux Oliveira Programa de Pós-Graduação em Engenharia Eletrônica, Universidade do Estado do Rio de Janeiro (UERJ), Rio de Janeiro – RJ
Gustavo Artur de Andrade Programa de Pós-Graduação em Engenharia de Automação e Sistemas, Universidade Federal de Santa catarina (UFSC), Florianópolis – SC

DOI: https://doi.org/10.20906/SBAI-SBSE-2023/3812

Keywords: Adaptive Control, Extremum Seeking, Partial Differential Equation, Averaging Theory, Backstepping in Infinite Dimensions

Abstract

This paper presents the design and analysis of gradient extremum seeking (ES) for scalar static maps, which are optimized in the presence of infinite-dimensional dynamics governed by Partial Diferential Equations (PDEs) of wave type containing a small amount of Kelvin-Voigt damping. This class of PDEs for extremum seeking has not been studied yet in the literature. We compensate the average-based actuation dynamics through a boundary controller via backstepping transformation. The local exponential convergence to a small neighborhood of the unknown optimal point is proven by means of an Input-to-State Stability (ISS) analysis as well as employing the averaging theory in infinite dimensions.