Controle Extremal Multivariável Estocástico do Tipo Newton com Atrasos Distintos de Entrada

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

doi:10.20906/SBAI-SBSE-2023/4048

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/SBAI-SBSE-2023/4048

Keywords: Stochastic Systems, Delays, Predictor, Multivariable Extremum Seeking, Newton Algorithm, Backstepping Transformation, Averaging Theory

Abstract

This paper proposes the design and analysis for a multivariable Newton-based stochastic extremum seeking control under delays. Multi-input systems with different time delays in each individual input channel are dealt with. A new predictor feedback with stochastic sinusoidal pertubation-based estimates of the Hessian’s inverse is incorporated in closed loop such that the convergence rate of the real-time optimizer can be made userassignable. Exponential stability and convergence to a small neighborhood of the unknown extremum point can be obtained. This result is rigorously reached by using backstepping transformation and averaging in infinite dimensions. A numerical example is shown in order to present the effectiveness of the proposed predictor-based stochastic extremum seeking for time-delay compensation.