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Journal ArticleDOI

On nonlinear detectability

TL;DR: In this paper, it was shown that the steady state property of the unobservable part of a given nonlinear dynamics is equivalent to the existence of a state detector (detectability).
Abstract: It is shown that the steady state property of the unobservable part of a given nonlinear dynamics is equivalent, under some boundedness assumptions, to the existence of a state detector (detectability). This property is illustrated, discussed and related to the existence of partial observers; local and global aspects are considered.
Citations
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Journal Article
TL;DR: In this paper, the authors proposed two methods for nonlinear observer design which are based on a partial non-linear observer canonical form (POCF), which provides the global asymptotic stability of error dynamics under a global Lipschitz and detectability-like condition.
Abstract: This paper proposes two methods for nonlinear observer design which are based on a partial nonlinear observer canonical form (POCF). Observability and integrability existence conditions for the new POCF are weaker than the well-established nonlinear observer canonical form (OCF), which achieves exact error linearization. The proposed observers provide the global asymptotic stability of error dynamics assuming that a global Lipschitz and detectability-like condition holds. Examples illustrate the advantages of the approach relative to the existing nonlinear observer design methods. The advantages of the proposed method include a relatively simple design procedure which can be broadly applied.

20 citations

Journal Article
TL;DR: In this paper, the observer design is carried out by means of a change of coordinates combined with a high gain technique, which results in an observer gain vector field which is extraordinary easy to compute.
Abstract: The paper proposes a method for observer design for a class of nonlinear systems. We decompose the system using a weaker concept than the relative degree. We provide sufficient conditions for global asymptotic stability of the error dynamics. The observer design is carried out by means of a change of coordinates combined with a high gain technique. In particular, our approach results in an observer gain vector field which is extraordinary easy to compute.

14 citations


Cites background from "On nonlinear detectability"

  • ...Assumption A4 means that the subsystem (3b) possesses a global steady state solution property [1]....

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  • ...Several approaches use Kalman-like decompositions, see [1, 17, 18, 26]....

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Journal ArticleDOI
TL;DR: This work considers the simultaneous reconstruction of the state vector and unknown parameters for a special class of non-linear parameter-dependent systems and suggests an approach that may be used for an online estimation of the unknown parameter.
Abstract: We consider the simultaneous reconstruction of the state vector and unknown parameters for a special class of non-linear parameter-dependent systems. The approach suggested here consists of two stages. First, the state is reconstructed by a reduced order unknown input observer. Second, this observer is augmented by a filter to obtain the desired parameter. The design procedure is straightforward and may be used for an online estimation of the unknown parameter. In contrast to previous work on adaptive systems, we do not require a persistence of excitation. The approach is illustrated on two non-linear cell models.

8 citations


Cites methods from "On nonlinear detectability"

  • ...In fact, several adaptive observer design methods rely on a similar decomposition (Besançon 2000), where condition A2 ensures local detectability of the system (Amicucci and Monaco 1998)....

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  • ...In fact, several adaptive observer design methods rely on a similar decomposition (Besançon 2000), where condition A2 ensures local detectability of the system (Amicucci and Monaco 1998)....

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Proceedings ArticleDOI
20 Oct 2011
TL;DR: In this article, an observer for field-oriented control for the speed-sensorless induction motor is proposed that works over the complete speed range and is stable at low and zero speed up to half rated load, even under strong resistance errors.
Abstract: An observer for field-oriented control for the speed-sensorless induction motor is proposed that works over the complete speed range. The speed is reconstructed with a nonlinear estimator based on the stator model and the stator current derivatives, and the rotor flux is calculated with an open-loop rotor model. Both reconstruction methods are combined in an asymptotic observer, for which convergence is proved analytically. In motor operation, the scheme is stable and fully converging for any speed, torque and excitation frequency including zero, which is an unobservable operation point. Restrictions appear in generator operation - the regenerative power is limited, and below nominal slip speed, torque is limited. Experiments are presented which confirm these results and highlight low- and zero-speed performance. The scheme is stable at low and zero speed up to half rated load, even under strong resistance errors.

8 citations


Cites background from "On nonlinear detectability"

  • ...The notion is extendable to nonlinear systems as well [ 5 ], where also observability singularities appear....

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Journal ArticleDOI
TL;DR: In this paper, the Entwurf nichtlinearer Zustandsbeobachter für eingangs-/ausgangslinearisierbare SISO-Systeme is presented.
Abstract: Abstract Der Beitrag behandelt den Entwurf nichtlinearer Zustandsbeobachter für eingangs-/ausgangslinearisierbare SISO-Systeme. Wie beim Reglerentwurf mittels Eingangs-/Ausgangs-Linearisierung wird vorausgesetzt, dass das System einen wohl definierten relativen Grad als auch eine asymptotisch stabile interne Dynamik besitzt. Der Beobachterentwurf erfolgt auf der Basis geeigneter Koordinatentransformationen in Verbindung mit einem High-Gain-Ansatz.

7 citations

References
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Book
01 Jan 1985
TL;DR: In this paper, a systematic feedback design theory for solving the problems of asymptotic tracking and disturbance rejection for linear distributed parameter systems is presented, which is intended to support the development of flight controllers for increasing the high angle of attack or high agility capabilities of existing and future generations of aircraft.
Abstract: : The principal goal of this three years research effort was to enhance the research base which would support efforts to systematically control, or take advantage of, dominant nonlinear or distributed parameter effects in the evolution of complex dynamical systems. Such an enhancement is intended to support the development of flight controllers for increasing the high angle of attack or high agility capabilities of existing and future generations of aircraft and missiles. The principal investigating team has succeeded in the development of a systematic methodology for designing feedback control laws solving the problems of asymptotic tracking and disturbance rejection for nonlinear systems with unknown, or uncertain, real parameters. Another successful research project was the development of a systematic feedback design theory for solving the problems of asymptotic tracking and disturbance rejection for linear distributed parameter systems. The technical details which needed to be overcome are discussed more fully in this final report.

8,525 citations

Book
01 Jan 1978
TL;DR: In this article, the authors consider non-linear differential equations with unique solutions, and prove the Kalman-Yacubovitch Lemma and the Frobenius Theorem.
Abstract: Introduction. Non-linear Differential Equations. Second-Order Systems. Approximate Analysis Methods. Lyapunov Stability. Input-Output Stability. Differential Geometric Methods. Appendices: Prevalence of Differential Equations with Unique Solutions, Proof of the Kalman-Yacubovitch Lemma and Proof of the Frobenius Theorem.

3,388 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that coprime right factorizations exist for the input-to-state mapping of a continuous-time nonlinear system provided that the smooth feedback stabilization problem is solvable for this system.
Abstract: It is shown that coprime right factorizations exist for the input-to-state mapping of a continuous-time nonlinear system provided that the smooth feedback stabilization problem is solvable for this system. It follows that feedback linearizable systems admit such fabrications. In order to establish the result, a Lyapunov-theoretic definition is proposed for bounded-input-bounded-output stability. The notion of stability studied in the state-space nonlinear control literature is related to a notion of stability under bounded control perturbations analogous to those studied in operator-theoretic approaches to systems; in particular it is proved that smooth stabilization implies smooth input-to-state stabilization. >

2,504 citations

Journal ArticleDOI
TL;DR: The properties of controllability, observability, and the theory of minimal realization for linear systems are well-understood and have been very useful in analyzing such systems as discussed by the authors.
Abstract: The properties of controllability, observability, and the theory of minimal realization for linear systems are well-understood and have been very useful in analyzing such systems. This paper deals with analogous questions for nonlinear systems.

2,306 citations

Journal ArticleDOI
TL;DR: In this paper, an observer for nonlinear systems is constructed under rather general technical assumptions (the fact that some functions are globally Lipschitz) and a tentative application to biological systems is described.
Abstract: An observer for nonlinear systems is constructed under rather general technical assumptions (the fact that some functions are globally Lipschitz). This observer works either for autonomous systems or for nonlinear systems that are observable for any input. A tentative application to biological systems is described. >

1,781 citations