Controle Extremal Multivariável Estocástico com Atrasos de Entrada e Saída

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.