On non-asymptotic observation of nonlinear systems

Reger, Johann; Sira-Ramírez, H.; Fliess, Michel

doi:10.1109/cdc.2005.1582824

Cited by 43 publications

(73 citation statements)

References 9 publications

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“…Such observers can be of important use for systems subject to disturbances or with inaccessible inputs, and in many applications such as fault detection and identification or parameter identification. Many different approaches have been considered to design unknown input observers: conventional Luenberger design procedure under some decoupling and detectability conditions [31,36,12] for linear systems, or high gain observers [29,8,37] and algebraic methods [52] in the nonlinear case.…”

Section: Introductionmentioning

confidence: 99%

Super twisting algorithm-based step-by-step sliding mode observers for nonlinear systems with unknown inputs

Floquet

Barbot

2007

International Journal of Systems Science

182

107

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. Super twisting algorithm based step-by-step sliding mode observers for nonlinear systems with unknown inputs. International Journal of Systems Science, Taylor Francis, 2007, 38 (10), pp.803-815. inria-00128137v2 Super twisting algorithm based step-by-step sliding mode observers for nonlinear systems with unknown inputsThis paper highlights the interest of step-by-step higher order sliding mode observers for MIMO nonlinear systems with unknown inputs. A structural matching condition, stating on the possibility to design such observers and to reconstruct the unknown inputs, is derived. A finite time sliding mode observer, based on the hierarchical use of the super twisting algorithm, is developed. Then, it is shown that this observer is of interest in the field of hybrid systems and systems with observability singularities. Lastly, it is shown through an example how to relax the usual matching condition by the means of this type of finite time sliding mode observer.

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Section: Introductionmentioning

confidence: 99%

Super twisting algorithm-based step-by-step sliding mode observers for nonlinear systems with unknown inputs

Floquet

Barbot

2007

International Journal of Systems Science

182

107

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“…Some steps of the derivation presented in [18] are now recalled for the sake of simplicity. Let us consider an arbitrary, analytic time signal yðtÞ; y : R þ 0 !…”

Section: Mathematical Frameworkmentioning

confidence: 99%

“…The use of operational calculus permits the influence of initial values to be eliminated, and a triangular system of equations is obtained which allows the respective signal time derivatives to be solved up to a certain desired order. The result is a general representation of a linear, time-varying output equation that allows an online-estimation of the required time derivatives [18]. As this approximation is only valid during a certain finite time interval, a periodic resetting of the calculations is necessary.…”

Section: Introductionmentioning

confidence: 99%

Control of a DC motor using algebraic derivative estimation with real time experiments

2014

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This paper presents an experimental control scheme for DC motors which combines an overlapping implementation of the algebraic derivative estimation method and a disturbance estimator based on the aforementioned algebraic derivative method. The methodol-ogy only requires the measurement of the angular position of the motor and the voltage input to the motor. The main advantages of the proposed approach are: it is independent of the motor's initial conditions, the methodology is robust to Coulomb friction effects, it does not require any statistical knowledge of the noises that corrupt the data, the deriva-tive estimation process does not require initial conditions or dependence between the sys-tem input and output, and the algorithm is computed online and in real time. The effectiveness of the proposed controller has been verified by means of computer simula-tions and it has also been experimentally implemented on a laboratory prototype with excellent results in both, stabilization and trajectory tracking tasks.

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“…See, e.g., Fliess et al, 2005b;Reger et al, 2005) for various applications to nonlinear systems (state and parametric estimations, fault-diagnosis and fault-tolerant control).…”

Section: Derivatives Of Noisy Signalsmentioning

confidence: 99%

Complex Continuous Nonlinear Systems: Their Black Box Identification and Their Control

Fliess

Join

Sira‐Ramírez

2006

IFAC Proceedings Volumes

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On non-asymptotic observation of nonlinear systems

Cited by 43 publications

References 9 publications

Super twisting algorithm-based step-by-step sliding mode observers for nonlinear systems with unknown inputs

Super twisting algorithm-based step-by-step sliding mode observers for nonlinear systems with unknown inputs

Control of a DC motor using algebraic derivative estimation with real time experiments

Complex Continuous Nonlinear Systems: Their Black Box Identification and Their Control

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