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Adaptive observer design for systems with incremental quadratic constraints and nonlinear outputs - application to chaos synchronization

Moysis Lazaros, Tripathi Meenakshi, Gupta Mahendra Kumar, Marwan Muhammad, Volos Christos

Archives of Control Sciences

2022

Vol. 32, No. 1

105--121

This work addresses the problem of adaptive observer design for nonlinear systems satisfying incremental quadratic constraints. The output of the system includes nonlinear terms, which puts an additional strain on the design and feasibility of the observer, which is guaranteed under the satisfaction of an LMI, and a set of algebraic constraints. A particular case where the output nonlinearity matches the unknown parameter coefficient is also discussed. The result is illustrated through a numerical example for the chaos synchronization of the Rössler system.

Robust observer design for Sugeno systems with incremental quadratic nonlinearity in the consequent

Moodi H., Farrokhi M.

International Journal of Applied Mathematics and Computer Science

2013

Vol. 23, no. 4

711--723

This paper is concerned with observer design for nonlinear systems that are modeled by T–S fuzzy systems containing parametric and nonparametric uncertainties. Unlike most Sugeno models, the proposed method contains nonlinear functions in the consequent part of the fuzzy IF-THEN rules. This will allow modeling a wider class of systems with smaller modelling errors. The consequent part of each rule contains a linear part plus a nonlinear term, which has an incremental quadratic constraint. This constraint relaxes the conservativeness introduced by other regular constraints for nonlinearities such as the Lipschitz conditions. To further reduce the conservativeness, a nonlinear injection term is added to the observer dynamics. Simulation examples show the effectiveness of the proposed method compared with the existing techniques reported in well-established journals.