Controle Extremal Multivariável Estocástico com Atrasos de Entrada e Saída

Paulo Cesar Souza da Silva; Paulo César Pellanda; Tiago Roux Oliveira

doi:10.20906/CBA2022/3234

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

DOI: https://doi.org/10.20906/CBA2022/3234

Keywords: Delays, Predictor, Extremum Seeking, Gradient Method, Backstepping Transformation, Averaging Theory

Abstract

This paper proposes the control design and analysis for a multivariable Gradient- based stochastic extremum seeking under delays. Multi-input systems with output delay and time delays in the input channels are dealt with. The phase compensation of the stochastic dither signals and a new predictor based on the estimate of the unknown Hessian are presented and incorporated in the closed-loop, allowing to achieve exponential stability and convergence to a small neighborhood of the unknown extremum point. This result is rigorously reached by using backstepping transformation and averaging in infinite dimensions. A numerical example is shown to illustrate the effectiveness of the proposed predictor-based stochastic extremum seeking for time-delay compensation.