Observer design for non-linear systems that are not uniformly observable

Jo, Nam-Hoon; Seo, Jae Hwa

doi:10.1080/00207170110112287

Cited by 28 publications

(23 citation statements)

References 12 publications

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“…Moreover, our results allow as well to apply additionally a diffeomorphism on the output space. Therefore, the necessary and sufficient geometrical conditions established in this paper are more general and quite different from those stated in Jo and Seo (2002) because of the introduction of commutativity of Lie bracket modulo a distribution.…”

Section: Introductionmentioning

confidence: 81%

“…Before dealing with this problem, let use highlight the fundamental difference between the proposed PONF with respect to the canonical form proposed in Jo and Seo (2002).…”

Section: Notation and Problem Statementmentioning

confidence: 99%

“…Thus, to design an observer for the proposed canonical form, one needs the Lipschitz condition to guarantee the estimation convergence. Jo and Seo (2002) provided necessary and sufficient geometrical conditions which guarantee the existence of a change of coordinates transforming a nonlinear dynamical system into a special partial observer normal form. This normal form is divided into two dynamical subsystems: the first one contains only a part of states which is of Brunovsky canonical form modulo output injection; the second one is nonlinear containing only the unobservable states and the output.…”

Section: Introductionmentioning

confidence: 99%

“…In order to relax the restriction of the result presented in Jo and Seo (2002), this paper proposes a more general PONF for a class of partially observable nonlinear systems. This new form is a generalization of the normal form studied in Jo and Seo (2002).…”

Section: Introductionmentioning

confidence: 99%

“…This new form is a generalization of the normal form studied in Jo and Seo (2002). The proposed PONF is divided as well into two subsystems, and we relax the form proposed in Jo and Seo (2002) by involving all states in the second subsystem. To deal with this generalization, we use the notion of commutativity of Lie bracket modulo a distribution.…”

Section: Introductionmentioning

confidence: 99%

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Partial observer normal form for nonlinear system

et al. 2016

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In this paper, we investigate the estimation problem for a class of partially observable nonlinear systems. For the proposed Partial Observer Normal Form (PONF), necessary and sufficient conditions are deduced to guarantee the existence of a change of coordinates which can transform the studied system into the proposed PONF. Examples are provided to illustrate the effectiveness of the proposed results.

show abstract

Section: Introductionmentioning

confidence: 81%

“…Before dealing with this problem, let use highlight the fundamental difference between the proposed PONF with respect to the canonical form proposed in Jo and Seo (2002).…”

Section: Notation and Problem Statementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Partial observer normal form for nonlinear system

et al. 2016

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Distributed observers design for a class of nonlinear systems to achieve omniscience asymptotically via differential geometry

Wang

et al. 2021

Intl J Robust & Nonlinear

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Distributed observers are the framework of fusing observed data by constructing a cooperative observer network. This article renders a scheme of distributed observers for a class of nonlinear system. With this scheme, each local nonlinear observer in the cooperative network can estimate the whole states of the underlying system by their own output measurements and information obtained from their neighbor via communication network. The proposed distributed observers are constructed with Partial Observable Canonical Form, which is a technology studied in differential geometry. The common observable subspace pruning and the weight matrix with spatial transformation are innovatively developed to solve the problem that each local observer is not in the same space. The sufficient conditions are proposed to guarantee the achievement of asymptotical omniscience of distributed nonlinear observers. Furthermore, our distributed observers can also be applied to linear systems and systems with some zero outputs. In addition, comparing with some existing methods of distributed nonlinear observers, our method admits some unbounded systems. Four simulations including multi‐Wen‐bridge oscillator systems, multi‐manipulators systems, unbounded nonlinear system and a linear system are employed to show the validity of the main result.

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Extended Luenberger Observer for Nonuniformly Observable Nonlinear Systems

Röbenack¹

Lecture Notes in Control and Information Science

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Observer design for non-linear systems that are not uniformly observable

Cited by 28 publications

References 12 publications

Partial observer normal form for nonlinear system

Partial observer normal form for nonlinear system

Distributed observers design for a class of nonlinear systems to achieve omniscience asymptotically via differential geometry

Extended Luenberger Observer for Nonuniformly Observable Nonlinear Systems

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