Análise e Projeto de Controladores Baseados no Método de Kernels de Aprendizado de Máquina para Sistemas de Dimensão Infinita Pertencentes à Classe de Callier-Desoer

Abstract

In this paper, we propose a methodology for the analysis and design of controllers for infinite-dimensional systems using finite-dimensional approximate models obtained through a data-driven kernel method. The results are developed under the assumption that the systems are stabilizable and detectable, ensuring the equivalence between internal and external stability, given that the approximate models represent only the input-output dynamics. We focus our approach on systems belonging to the Callier-Desoer class, which have only a finite number of unstable poles and an infinite number of stable poles. By identifying the system model using the kernel algorithm and leveraging its convergence results, we ensure that the error between the output of the finite-dimensional approximate model and the output of the original system is bounded. Consequently, by designing a robust controller with a robustness margin greater than the sum of the identification error and the upper bound associated with the unidentified stable infinite-dimensional dynamics of the plant, we guarantee that the control system, designed based on the finite approximation, will stabilize the original infinite-dimensional system.