Nonlinear observer design using Lyapunov’s auxiliary theorem

Kazantzis, Nikolaos; Kravaris, Costas

doi:10.1016/s0167-6911(98)00017-6

Cited by 381 publications

(203 citation statements)

References 13 publications

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“…Such systems take the general form: [17] or the design of Kazantzis-Kravaris observers [18] lead to an approximate form that can be represented by (1) with ω(t) representing an unstructured uncertainty arising from the approximation.…”

Section: Remarkmentioning

confidence: 99%

Set‐based adaptive estimation for a class of uncertain nonlinear systems with output dependent nonlinearities

Dhaliwal

Guay

2014

Can J Chem Eng

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In this article, we consider the problem of parameter identification and state estimation of an uncertain continuous-time linearly parameterized nonlinear system with output dependent nonlinearities subject to exogenous disturbances. A set-based adaptive estimation is proposed in which the parameters and the states of the system are estimated along with an uncertainty set guaranteed to contain the true unknown values. The setupdate approach is such that the sets are updated only when an improvement in the precision of the parameter estimates and the state estimates can be guaranteed. The formulation provides robustness to parameter estimation error and bounded disturbances. The adaptive estimation technique can be viewed as an adaptive interval observer. Simulation examples are used to illustrate the effectiveness of the developed procedure and ascertain the theoretical results.

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Section: Remarkmentioning

confidence: 99%

Set‐based adaptive estimation for a class of uncertain nonlinear systems with output dependent nonlinearities

Dhaliwal

Guay

2014

Can J Chem Eng

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“…We consider a generalization of the approach of [9] to develop a set of conditions that are necessary and sufficient for the solution of a general observer linearization problem in which both output-dependent diffeomorphisms and output-dependent time-scaling transformations are considered. Although the problem is not as general as the problem treated in [11] and [12], the study demonstrates that the class of nonlinear systems that are diffeomorphic to systems whose error dynamics are linear can be extended by considering a simultaneous change of output and time-scale transformation. The main result of this paper confirms that the application of a combined output diffeomorphism and a time-scale transformation allows one to tackle a more general class of systems.…”

Section: Introductionmentioning

confidence: 99%

“…In [11] and [12], the observer linearization problem was addressed in its most general formulation. Conditions are derived for the existence of an approximate solution to a nonlinear partial differential equation whose solution provides a state-space diffeomorphism that transforms the system into an observer with approximately linear error dynamics.…”

Section: Introductionmentioning

confidence: 99%

Observer Linearization of Nonlinear Systems by Generalized Tansformations

Guay

2008

Asian Journal of Control

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In this paper, we study the problem of observer linearization for single output dynamical systems in the presence of an output-dependent time-scaling transformation and a simultaneous output diffeomorphism. The approach, based on an exterior calculus approach, provides a constructive approach to the problem of equivalence of a locally observable nonlinear system to a linear observer form by means of an output dependent time-scale transformation, an output diffeomorphism and a state-space diffeomorphism. A generalization of existing results is obtained which allows the treatment of a larger class of locally observable nonlinear systems.

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“…This approach was developed through a Lyapunov-based observer from the work of Kazantzis and Kravaris. 12 The preceding finite time observer design approaches were carried out without considering disturbances in the measurements or dynamics. Such disturbances are usually present in practical applications and they affect measurements and can be state dependent.…”

Section: Introductionmentioning

confidence: 99%

Finite time estimation through a continuous‐discrete observer

Mazenc

Ahmed

Malisoff

2018

Intl J Robust & Nonlinear

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Summary We study two broad classes of nonlinear time‐varying continuous‐time systems with outputs. For the first class, we build an observer in the case where a state dependent disturbance affects the linear approximation. When the disturbances are the zero functions, our observer provides exact values of the state at all times larger than a suitable finite time, and it provides an approximate estimate when there are nonzero disturbances, so our observers are called finite time observers. We use this construction, which is of interest for its own sake, to design a globally exponentially stabilizing dynamic output feedback for a family of nonlinear systems whose outputs are only available on some finite time intervals. Our simulations illustrate the efficacy of our methods.

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Nonlinear observer design using Lyapunov’s auxiliary theorem

Cited by 381 publications

References 13 publications

Set‐based adaptive estimation for a class of uncertain nonlinear systems with output dependent nonlinearities

Set‐based adaptive estimation for a class of uncertain nonlinear systems with output dependent nonlinearities

Observer Linearization of Nonlinear Systems by Generalized Tansformations

Finite time estimation through a continuous‐discrete observer

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