Exact State Reconstruction for LTI-Systems with Non-Differentiable Unknown Inputs

Tranninger, Markus; Seeber, Richard; Steinberger, Martin; Horn, Martin

doi:10.23919/ecc.2019.8796142

Cited by 8 publications

(21 citation statements)

References 13 publications

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“…It is well known that strong * detectability is the minimum requirement for the existence of a linear unknown input observer [3], whereas strong detectability is the minimum requirement for (at least asymptotically) reconstructing the state with any estimation scheme [19]. If the system is strongly observable, it is possible to exactly reconstruct the state within finite or fixed time by employing higher-order sliding mode techniques [20,19,15]. The following relations are stated in [3].…”

Section: Strong Detectability and Observabilitymentioning

confidence: 99%

“…It follows directly from the construction of the proposed observer that the number of differentiation operations is minimal. The design is straightforward and does not require a "stabilizing" Luenberger observer as in previous works [15,19,20]. Hence, its observer order corresponds to the system order.…”

Section: Introductionmentioning

confidence: 98%

“…If the system is strongly detectable [3] but the observer matching condition is not fulfilled, it is still possible to estimate the states by taking higher order derivatives of the output signal into account [15]. Popular techniques for obtaining such derivatives are based on higher order sliding mode techniques and in particular on Levant's arbitrary order robust exact differentiator [16].…”

Section: Introductionmentioning

confidence: 99%

“…It is based on successive differentiation of the output vector and the decoupling from the influence of the unknown inputs. The approach was extended in order to employ higher order sliding mode differentiators [15,19,20,21]. This improves the accuracy of the obtained estimates w.r.t.…”

Section: Introductionmentioning

confidence: 99%

“…discretization and bounded measurement noise [9]. All mentioned higher order sliding mode approaches require a Luenberger observer cascaded with the sliding mode reconstruction scheme in order to fulfill the requirements for the higher order sliding mode differentiators [15]. Hence, such estimation schemes require at least twice the number of states of the considered system.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Unknown Input Observer Design for Linear Time-Invariant Systems -- A Unifying Framework

Tranninger¹,

Niederwieser²,

Seeber³

et al. 2021

Preprint

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This paper presents a new observer design approach for linear time invariant multivariable systems subject to unknown inputs. The design is based on a transformation to the so-called special coordinate basis. This form reveals important system properties like invertability or the finite and infinite zero structure. Depending on the system's strong observability properties, the special coordinate basis allows for a straightforward unknown input observer design utilizing linear or nonlinear observers design techniques. The chosen observer design technique does not only depend on the system properties, but also on the desired convergence behavior of the observer. Hence, the proposed design procedure can be seen as a unifying framework for unknown input observer design.

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Section: Strong Detectability and Observabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Unknown Input Observer Design for Linear Time-Invariant Systems -- A Unifying Framework

Tranninger¹,

Niederwieser²,

Seeber³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Unknown input observer design for linear time‐invariant systems—A unifying framework

Tranninger

Niederwieser

Seeber

et al. 2022

Intl J Robust & Nonlinear

Self Cite

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This article presents a new observer design approach for linear time invariant multivariable systems subject to unknown inputs. The design is based on a transformation to the so‐called special coordinate basis (SCB). This form reveals important system properties like invertability or the finite and infinite zero structure. Depending on the system's strong observability properties, the SCB allows for a straightforward unknown input observer design utilizing linear or nonlinear observers design techniques. The chosen observer design technique does not only depend on the system properties, but also on the desired convergence behavior of the observer. Hence, the proposed design procedure can be seen as a unifying framework for unknown input observer design.

show abstract

Strong observability as a sufficient condition for non-singularity and lossless convexification in optimal control with mixed constraints

Kunhippurayil

Harris

2022

Control Theory Technol.

View full text Add to dashboard Cite

Exact State Reconstruction for LTI-Systems with Non-Differentiable Unknown Inputs

Cited by 8 publications

References 13 publications

Unknown Input Observer Design for Linear Time-Invariant Systems -- A Unifying Framework

Unknown Input Observer Design for Linear Time-Invariant Systems -- A Unifying Framework

Unknown input observer design for linear time‐invariant systems—A unifying framework

Strong observability as a sufficient condition for non-singularity and lossless convexification in optimal control with mixed constraints

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