An observer looks at synchronization

Nijmeijer, Henk; Mareels, Iven

doi:10.1109/81.633877

Cited by 629 publications

(326 citation statements)

References 35 publications

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“…The synchronization problem has been recognized of great interest recently [16,6] and a link has been made between synchronization and observation theories, mostly by Nijmeijer and his group [17,18]. The observer theory, coming from the control theory, has been introduced in the early seventies by Luenberger [19] in the linear case; in the non-linear case, some partial results exist [20].…”

Section: Synchronization and Observationmentioning

confidence: 99%

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Online generation of cyclic leg trajectories synchronized with sensor measurement

Héliot

Espiau

2008

Robotics and Autonomous Systems

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The generation of trajectories for a biped robot is a problem which has been largely studied for several years, and many satisfying off-line solutions exist for steady-state walking in absence of disturbances. The question is a little more complex when the generation of the desired trajectories of joints or links has to be achieved or adapted online, i.e. in real time, for example when it is wished to strongly synchronize these trajectories with an external motion. This is precisely the problem addressed in this paper. Indeed, we consider the case where the "master" motion is measured by an position sensor embedded on a human leg. We propose a method to synchronize the motion of a robot or on other device with respect to the output signal of the sensor. The main goal is to estimate as accurately as possible the current phase along the gait cycle. We use for that purpose a model based on a nonlinear oscillator, to which we associate an observer. Introducing the sensor output in the observer allows us to compute the oscillator phase and to generate a synchronized multilinks trajectory, at a very low computational cost. The paper also presents evaluation results in terms of robustness against parameter estimation errors and velocity changes in the input.

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Section: Synchronization and Observationmentioning

confidence: 99%

“…The reduced observer will in some sense tend to track a transformation of the state variable to be estimated, namely x 2 . In the same spirit as [17] does, we introduce the variable z:…”

Section: Observer Designmentioning

confidence: 99%

Online generation of cyclic leg trajectories synchronized with sensor measurement

Héliot

Espiau

2008

Robotics and Autonomous Systems

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“…The classical approach to nonlinear observer design consists in finding a transformation that linearizes the plant up to an output injection term and then applying standard linear observer design techniques, see [2] and [3]. We refer the reader to [4] and references therein for a fairly complete literature review of the existing observer design techniques for nonlinear systems. More recently, in [5] and [6], the early ideas of Luenberger are extended to the nonlinear case.…”

Section: Introductionmentioning

confidence: 99%

Immersion and invariance observers with time-delayed output measurements

Murguía

Fey

Nijmeijer

2016

Communications in Nonlinear Science and Numerical Simulation

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“…Such an issue has been presented from a control theoretic point of view as a state reconstruction problem and has constituted a milestone for deeper insights. A relevant survey on chaos synchronization dealing with the observer approach can be found in [11]. For recent advanced techniques to achieve synchronization, the reader is referred to [12] for observers with linearizable dynamics, to [13] for observers derived from the concept of absolute stability , to [14] for observers dedicated to systems having a Generalized Hamiltonian Form, or to a plethora of papers dealing with the Extended Kalman Filter based methods.…”

Section: Introductionmentioning

confidence: 99%

Considering the attractor structure of chaotic maps for observer-based synchronization problems

Millérioux

Anstett

Bloch

2005

Mathematics and Computers in Simulation

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To cite this version:Gilles Millérioux, Floriane Anstett, Gérard Bloch. Considering the attractor structure of chaotic maps for observer-based synchronization problems. AbstractThe main purpose of this paper is to state some sufficient conditions for global synchronization of chaotic maps. The synchronization is viewed as a state reconstruction problem which is tackled by polytopic observers. Unlike most standard observers, polytopic observers can account for a special property of chaotic dynamics. Indeed, it is shown that many chaotic maps can be described in a so-called convexified form, involving a time-varying parameter which depends on the chaotic state vector. Such a form makes it possible to incorporate knowledge on the structure of the compact set wherein the parameter lies. This set depends implicitly on the structure of the chaotic attractor. It is proved that the conservatism of the polyquadratic stability conditions for the state reconstruction, stated in a companion paper, can be reduced when the corresponding Linear Matrix Inequalities involve the vertices of the minimal convex hull of this set. Theoretical developments along with special emphasis on computational aspects are provided and illustrated in the context of adaptive synchronization.

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An observer looks at synchronization

Cited by 629 publications

References 35 publications

Online generation of cyclic leg trajectories synchronized with sensor measurement

Online generation of cyclic leg trajectories synchronized with sensor measurement

Immersion and invariance observers with time-delayed output measurements

Considering the attractor structure of chaotic maps for observer-based synchronization problems

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