Transformation of nonlinear systems in observer canonical form with reduced dependency on derivatives of the input

Proychev, Todor Ph.; Mishkov, R. L.

doi:10.1016/0005-1098(93)90145-j

Cited by 36 publications

(6 citation statements)

References 11 publications

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“…Thus, the same map H in different compositions (17) and (19) commuting the same isomorphism F has different inverses (18) and (20) and these inverses are the only ones in their compositions. The algebraic principle of relativity in relation to the theory of systems is interpreted in [3] as follows: the same element (characterized by some mapping) in combination with different elements in different systems can exhibit different properties and even properties that it did not have outside the system at all-for example, the property of having an inverse map to the map being its model.…”

Section: Discussionmentioning

confidence: 99%

A General Principle of Isomorphism: Determining Inverses

Kulabukhov¹

2019

Symmetry

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The problem of determining inverses for maps in commutative diagrams arising in various problems of a new paradigm in algebraic system theory based on a single principle—the general principle of isomorphism is considered. Based on the previously formulated and proven theorem of realization, the rules for determining the inverses for typical cases of specifying commutative diagrams are derived. Simple examples of calculating the matrix maps inverses, which illustrate both the derived rules and the principle of relativity in algebra based on the theorem of realization, are given. The examples also illustrate the emergence of new properties (emergence) in maps in commutative diagrams modeling (realizing) the corresponding systems.

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Section: Discussionmentioning

confidence: 99%

A General Principle of Isomorphism: Determining Inverses

Kulabukhov¹

2019

Symmetry

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“…u, to obtain generalized lower-triangular forms for which high-gain theory may be applied. See, e.g., [237,99,188,204,52] and references therein. For instance, one can allow the state transformation (53) to be t dependent (resp.…”

Section: Differential Observability and Normal Formsmentioning

confidence: 99%

Observer design for continuous-time dynamical systems

Bernard

Andrieu

Astolfi

2022

Annual Reviews in Control

106

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We review the main design techniques of state observer design for continuous-time dynamical systems, namely algorithms which reconstruct online the full information of a dynamical process on the basis of partially measured data. Starting from necessary conditions for the existence of such asymptotic observers, we classify the available methods depending on the detectability/observability assumptions they require. We show how each class of observer relies on transforming the system dynamics in a particular normal form which allows the design of an observer, and how each observability condition guarantees the invertibility of its associated transformation and the convergence of the observer. Finally, some implementation aspects and open problems are briefly discussed.

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“…Availability of input and output derivatives also affects the effectiveness of the nonlinear observers. Some researchers have tried to reduce the dependency of the non‐linear observers on the derivatives of the input and the output .…”

Section: Introductionmentioning

confidence: 99%

Observability Analysis of Continuous‐Time LTI Systems with Limited Derivative Data

Eskandari¹,

Oishi²,

Wang³

2013

Asian Journal of Control

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We consider continuous-time LTI systems with either unknown-input or with lack of information about the input and output derivatives. We compute the unknown-input observability subspace and the observability subspace with unknown derivatives of input and output. We first formulate the unknown-input observability subspace via projection matrices, then show that through having the unknowninput observability subspace, one can easily evaluate the effect of known input and output signals but unknown derivatives on the observability subspace. Our method is demonstrated on the dynamics of a longitudinal aircraft in steady-state flight.

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Transformation of nonlinear systems in observer canonical form with reduced dependency on derivatives of the input

Cited by 36 publications

References 11 publications

A General Principle of Isomorphism: Determining Inverses

A General Principle of Isomorphism: Determining Inverses

Observer design for continuous-time dynamical systems

Observability Analysis of Continuous‐Time LTI Systems with Limited Derivative Data

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