Tutorial on arbitrary and state-dependent sampling

Fiter, Christophe; Omran, Hassan; Hetel, Laurentiu; Richard, Jean‐Pierre

doi:10.1109/ecc.2014.6862643

Cited by 5 publications

(8 citation statements)

References 80 publications

(106 reference statements)

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“…Theorem 1 Consider the sampled-data system 5under hypotheses H.1-H.4, and the equivalent representation (9), (10). Consider the notations y(t) and w(t) defined in (9) and 10, respectively.…”

Section: Resultsmentioning

confidence: 99%

“…Intuitively, the sampling interval must be sufficiently small to ensure the stability [20,6]. Still, in practice it is difficult to maintain a constant sampling period during real-time control and the variations of the sampling interval may have a destabilizing effect [10,13], even for small sampling intervals. A quantitative estimation of the so-called Maximum Sampling Interval MSI that ensures stability (under timevarying sampling intervals), is very important from the practical point of view.…”

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confidence: 99%

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Stability analysis of some classes of input-affine nonlinear systems with aperiodic sampled-data control

et al. 2016

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International audienceIn this paper we investigate the stability analysis of nonlinear sampled-data systems, which are affine in the input. We assume that a stabilizing controller is designed using the emulation technique. We intend to provide sufficient stability conditions for the resulting sampled-data system. This allows to find an estimate of the upper bound on the asynchronous sampling intervals, for which stability is ensured. The main idea of the paper is to address the stability problem in a new framework inspired by the dissipativity theory. Furthermore, the result is shown to be constructive. Numerically tractable criteria are derived using linear matrix inequality for polytopic systems and using sum of squares technique for the class of polynomial systems

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Section: Resultsmentioning

confidence: 99%

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confidence: 99%

Stability analysis of some classes of input-affine nonlinear systems with aperiodic sampled-data control

et al. 2016

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“…1) Camera inputs constraints: First, constraints on the control input are included in the domain K as: (16) to ensure the camera velocity will not exceed its physical limitations, with u − c = (u − cx , u − cy ) and u + c = (u + cx , u + cy ). Obviously, these constraints are applied for all the set of inputs − → u c .…”

Section: B Constraintsmentioning

confidence: 99%

“…A link can be established between our method and the selftriggered control in the sense that the quantity of information sent by the camera to the ground robots is intentionally reduced [16]. Indeed at each sampling instant the knowledge of the UAV and of the robots dynamics allows to predict the camera velocity without any measurement.…”

Section: Introductionmentioning

confidence: 99%

Visual servoing using model predictive control to assist multiple trajectory tracking

Cazy¹,

Wieber²,

Giordano³

et al. 2017

2017 IEEE International Conference on Robotics and Automation (ICRA)

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We propose in this paper a new active perception scheme based on Model Predictive Control under constraints for generating a sequence of visual servoing tasks. The proposed control scheme is used to compute the motion of a camera whose task is to successively observe a set of robots for measuring their position and improving the accuracy of their localization. This method is based on the prediction of an uncertainty model (due to actuation and measurement noise) for determining which robot has to be observed by the camera. Simulation results are presented for validating the approach.

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“…In the literature, two main research lines consider this aspect. Stability analysis under arbitrary time-varying sampling: In the past decade, several works concerning the robust stability analysis of sampled-data systems with arbitrary time-varying sampling have been proposed (see [10] for a short survey), based on Impulsive delay differential Equations [34,12,11,20,32], on Input-Output approaches [26,13,28], on Hybrid approaches [27,18], and on Discrete-time / Convex embeddings [16,5,17].…”

Section: Introductionmentioning

confidence: 99%

A robust stability framework for LTI systems with time-varying sampling

et al. 2015

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International audienceThis work aims at enlarging the sampling intervals in several state feedback control situations by designing a sampling map in the state space. We consider the case of linear time invariant (LTI) systems with state-bounded perturbations, and guarantee their exponential stability for a chosen decay-rate. The approach is based on linear matrix inequalities (LMIs) obtained thanks to Lyapunov-Razumikhin stability conditions and convexification arguments. First, it enables to optimize the lower-bound of the sampling maps by computing the adequate Lyapunov-Razumikhin function. This result can be interpreted as a robust stability analysis with respect to arbitrary time-varying sampling intervals, which may be useful in the case of uncontrolled sampling, or in the presence of phenomenon such as sampling jitter. Then, the obtained results are extended to design the sampling map in three dynamic sampling control situations: event-triggered control, self-triggered control, and state-dependent sampling. The results are illustrated with a numerical example from the literature

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Tutorial on arbitrary and state-dependent sampling

Cited by 5 publications

References 80 publications

Stability analysis of some classes of input-affine nonlinear systems with aperiodic sampled-data control

Stability analysis of some classes of input-affine nonlinear systems with aperiodic sampled-data control

Visual servoing using model predictive control to assist multiple trajectory tracking

A robust stability framework for LTI systems with time-varying sampling

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