On Estimation and observer design in nonlinear systems : theory and application
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Date
2022
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Universite Mouloud MAMMERI Tizi-Ouzou
Abstract
Abstract :
The work conducted in this thesis contributes to the state of the art on observer design for nonlinear systems. The main objective is to design a high-gain like observer for a class of nonlinear systems with delayed output measurements. To overcome some limitations of the standard high-gain observer and enhance the time response, two high-gain like observer approaches have been proposed.
In the first part, we present a high-gain observer design for nonlinear systems with time-varying delayed output measurements. Based on a recent high-gain like observer design method, called HG/LMI observer, a larger bound of the time-delay is allowed compared to that obtained by using the standard high-gain methodology. Such a HG/LMI observer adopts a lower value of the tuning parameter, which results in the reduction of the observer’s gain value and an increase in the maximum bound of the delay required to ensure exponential convergence. An application to nonlinear systems with sampled measurements is provided. Furthermore, the proposed methodology is extended to systems with nonlinear outputs.
The second part is dedicated to the design of a prescribed-time high-gain observer that achieves stability in a predefined time. The fixed time convergence of the observer within a prescribed time is shown through a Lyapunov differential inequality and a state transformation that involves a scaling function. The observer’s gain depends on a time-varying function monotonically increasing to infinity as the time tends to the predefined time of convergence. Moreover, the proposed observer reduces the peaking phenomenon, which is one of the main limitations of the high-gain observer design.
In the last part, an application of the proposed high-gain approaches to estimate the water level in the Coupled Tanks system is presented. Extensive numerical simulations are provided to show the effectiveness of the HG/LMI observer and the prescribed-time high-gain observer. Furthermore, a comparison with the standard high-gain observer is established to demonstrate the superiority of the proposed observer design approaches in reducing the peaking phenomena and enhancing the estimation convergence error, respectively.
Description
101f. : ill. ; 30cm. + CD Rom
Keywords
High-gain observer, Linear matrix inequalities, Lyapunov-Krasovskii functional, Nonlinear systeme
Citation
Analyse Mathématique et Applications