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Article

H∞ State and Parameter Estimation for Lipschitz Nonlinear Systems

by
Pedro Eusebio Alvarado-Méndez
1,
Carlos M. Astorga-Zaragoza
1,*,
Gloria L. Osorio-Gordillo
1,
Adriana Aguilera-González
2,
Rodolfo Vargas-Méndez
1 and
Juan Reyes-Reyes
1
1
Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Cuernavaca 62490, Morelos, Mexico
2
ESTIA Institute of Technology, University of Bordeaux, F-64210 Bidart, France
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2024, 29(4), 51; https://doi.org/10.3390/mca29040051
Submission received: 29 May 2024 / Revised: 2 July 2024 / Accepted: 2 July 2024 / Published: 4 July 2024
(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2024)
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Abstract

A H∞ robust adaptive nonlinear observer for state and parameter estimation of a class of Lipschitz nonlinear systems with disturbances is presented in this work. The objective is to estimate parameters and monitor the performance of nonlinear processes with model uncertainties. The behavior of the observer in the presence of disturbances is analyzed using Lyapunov stability theory and by considering an H∞ performance criterion. Numerical simulations were carried out to demonstrate the applicability of this observer for a semi-active car suspension. The adaptive observer performed well in estimating the tire rigidity (as an unknown parameter) and induced disturbances representing damage to the damper. The main contribution is the proposal of an alternative methodology for simultaneous parameter and actuator disturbance estimation for a more general class of nonlinear systems.
Keywords: adaptive observer; nonlinear system; Lipschitz nonlinearities adaptive observer; nonlinear system; Lipschitz nonlinearities

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MDPI and ACS Style

Alvarado-Méndez, P.E.; Astorga-Zaragoza, C.M.; Osorio-Gordillo, G.L.; Aguilera-González, A.; Vargas-Méndez, R.; Reyes-Reyes, J. H∞ State and Parameter Estimation for Lipschitz Nonlinear Systems. Math. Comput. Appl. 2024, 29, 51. https://doi.org/10.3390/mca29040051

AMA Style

Alvarado-Méndez PE, Astorga-Zaragoza CM, Osorio-Gordillo GL, Aguilera-González A, Vargas-Méndez R, Reyes-Reyes J. H∞ State and Parameter Estimation for Lipschitz Nonlinear Systems. Mathematical and Computational Applications. 2024; 29(4):51. https://doi.org/10.3390/mca29040051

Chicago/Turabian Style

Alvarado-Méndez, Pedro Eusebio, Carlos M. Astorga-Zaragoza, Gloria L. Osorio-Gordillo, Adriana Aguilera-González, Rodolfo Vargas-Méndez, and Juan Reyes-Reyes. 2024. "H∞ State and Parameter Estimation for Lipschitz Nonlinear Systems" Mathematical and Computational Applications 29, no. 4: 51. https://doi.org/10.3390/mca29040051

APA Style

Alvarado-Méndez, P. E., Astorga-Zaragoza, C. M., Osorio-Gordillo, G. L., Aguilera-González, A., Vargas-Méndez, R., & Reyes-Reyes, J. (2024). H∞ State and Parameter Estimation for Lipschitz Nonlinear Systems. Mathematical and Computational Applications, 29(4), 51. https://doi.org/10.3390/mca29040051

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