Adaptive estimation for uncertain nonlinear systems with measurement noise: A sliding-mode observer approach

Roberto Franco; Héctor Ríos; Denis Efimov; Wilfrid Perruquetti

doi:10.1002/rnc.5220

Adaptive estimation for uncertain nonlinear systems with measurement noise: A sliding-mode observer approach

Roberto Franco, Héctor Ríos, Denis Efimov, Wilfrid Perruquetti

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10 Scopus citations

Abstract

This article deals with the problem of adaptive estimation, that is, the simultaneous estimation of the state and time-varying parameters, in the presence of measurement noise and state disturbances, for a class of uncertain nonlinear systems. An adaptive observer is proposed based on a nonlinear time-varying parameter identification algorithm and a sliding-mode observer. The nonlinear time-varying parameter identification algorithm provides a fixed-time rate of convergence, to a neighborhood of the origin, while the sliding-mode observer ensures ultimate boundedness for the state estimation error attenuating the effects of the external disturbances. Linear matrix inequalities are provided for the synthesis of the adaptive observer while the convergence proofs are given based on the Lyapunov and input-to-state stability theory. Finally, some simulation results show the feasibility of the proposed approach.

Original language	English
Pages (from-to)	3809-3826
Number of pages	18
Journal	International Journal of Robust and Nonlinear Control
Volume	31
Issue number	9
DOIs	https://doi.org/10.1002/rnc.5220
State	Published - Jun 2021

Bibliographical note

Funding Information:
R. Franco and H. Ríos thank the financial support from CONACYT CVU 772057, and Cátedras CONACYT CVU 270504 project 922, respectively, and from TECNM project 8417.20‐P.

Funding Information:
Consejo Nacional de Ciencia y Tecnología, CVU 772057; Consejo Nacional de Ciencia y Tecnología, Cítedras CONACYT CVU 270504 project 922; Tecnológico Nacional de México, project 8417.20‐P; Government of Russian Federation, Grant 08‐08; Ministry of Science and Higher Education of Russian Federation, passport of goszadanie, no. 2019‐0898 Funding information

Funding Information:
D. Efimov thanks the financial support by the Government of Russia Federation (Grant 08‐08) and by the Ministry of Science and Higher Education of Russian Federation, passport of goszadanie no. 2019‐0898.

Funding Information:
information Consejo Nacional de Ciencia y Tecnología, CVU 772057; Consejo Nacional de Ciencia y Tecnología, Cítedras CONACYT CVU 270504 project 922; Tecnológico Nacional de México, project 8417.20-P; Government of Russian Federation, Grant 08-08; Ministry of Science and Higher Education of Russian Federation, passport of goszadanie, no. 2019-0898R. Franco and H. Ríos thank the financial support from CONACYT CVU 772057, and Cátedras CONACYT CVU 270504 project 922, respectively, and from TECNM project 8417.20-P. D. Efimov thanks the financial support by the Government of Russia Federation (Grant 08-08) and by the Ministry of Science and Higher Education of Russian Federation, passport of goszadanie no. 2019-0898.

Publisher Copyright:
© 2020 John Wiley & Sons Ltd

Keywords

adaptive observer
nonlinear systems
sliding-modes

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10.1002/rnc.5220

Cite this

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abstract = "This article deals with the problem of adaptive estimation, that is, the simultaneous estimation of the state and time-varying parameters, in the presence of measurement noise and state disturbances, for a class of uncertain nonlinear systems. An adaptive observer is proposed based on a nonlinear time-varying parameter identification algorithm and a sliding-mode observer. The nonlinear time-varying parameter identification algorithm provides a fixed-time rate of convergence, to a neighborhood of the origin, while the sliding-mode observer ensures ultimate boundedness for the state estimation error attenuating the effects of the external disturbances. Linear matrix inequalities are provided for the synthesis of the adaptive observer while the convergence proofs are given based on the Lyapunov and input-to-state stability theory. Finally, some simulation results show the feasibility of the proposed approach.",

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AB - This article deals with the problem of adaptive estimation, that is, the simultaneous estimation of the state and time-varying parameters, in the presence of measurement noise and state disturbances, for a class of uncertain nonlinear systems. An adaptive observer is proposed based on a nonlinear time-varying parameter identification algorithm and a sliding-mode observer. The nonlinear time-varying parameter identification algorithm provides a fixed-time rate of convergence, to a neighborhood of the origin, while the sliding-mode observer ensures ultimate boundedness for the state estimation error attenuating the effects of the external disturbances. Linear matrix inequalities are provided for the synthesis of the adaptive observer while the convergence proofs are given based on the Lyapunov and input-to-state stability theory. Finally, some simulation results show the feasibility of the proposed approach.

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Adaptive estimation for uncertain nonlinear systems with measurement noise: A sliding-mode observer approach

Abstract

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