Robust State-Feedback Control and Convergence Analysis for Uncertain LPV Systems Using State and Parameter Estimation

Esdras Battosti da Silva, Ruhan Pontes Policarpo de Souza, Cristiano Marcos Agulhari (), Glaucia Maria Bressan and Wesley Angelino de Souza
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Esdras Battosti da Silva: Academic Department of Electrical Engineering, Universidade Tecnológica Federal do Paraná—(UTFPR), Cornelio Procopio 86300-000, Brazil
Ruhan Pontes Policarpo de Souza: Graduate Program in Electrical Engineering, Universidade Tecnológica Federal do Paraná—(UTFPR), Cornelio Procopio 86300-000, Brazil
Cristiano Marcos Agulhari: Graduate Program in Electrical Engineering, Universidade Tecnológica Federal do Paraná—(UTFPR), Cornelio Procopio 86300-000, Brazil
Glaucia Maria Bressan: Graduate Program in Bioinformatics, Universidade Tecnológica Federal do Paraná—(UTFPR), Cornelio Procopio 86300-000, Brazil
Wesley Angelino de Souza: Graduate Program in Electrical Engineering, Universidade Tecnológica Federal do Paraná—(UTFPR), Cornelio Procopio 86300-000, Brazil

Mathematics, 2024, vol. 12, issue 13, 1-24

Abstract: This study introduces the design of a state-feedback controller for Linear Parameter Varying (LPV) systems in scenarios where exogenous parameters are not directly accessible, and the state vector is to be estimated. Instead of considering a static feedback gain, it proposes a method for estimating these parameters and synthesizing a parameter-dependent state-feedback gain that is robust against uncertainties in parameter estimation. The state vector used by the state-feedback controller, and some quantities required by the estimation law, are both obtained by a robust filter synthesized by LMI (Linear Matrix Inequalities). This paper outlines the estimation, filtering, and control laws, detailing the conditions necessary for ensuring convergence and stability. A numerical experiment and a 2 DoF torsional system application show the enhanced dynamic performance of the method when applied to uncertain dynamic systems. The findings highlight the effectiveness of the proposed approach in maintaining system stability and improving performance despite the inherent uncertainties in parameter estimation, offering a significant contribution to the field of robust control for LPV systems.

Keywords: LPV systems; parametric estimation; state-feedback control; linear matrix inequalities; robust filtering; estimation uncertainty (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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