Event-triggered damping of a linear wave equation

Baudouin, Lucie; Marx, Swann; Tarbouriech, Sophie

doi:10.1016/j.ifacol.2019.08.011

Cited by 16 publications

(18 citation statements)

References 19 publications

(22 reference statements)

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“…Meanwhile, to better solving the Zeno problem, the function η i (t) in the event-triggered condition must be positive. erefore, the piecewise function η i (t) in equation ( 25) is a good selection which is different from the exponential function in literatures [45,46].…”

Section: Remarkmentioning

confidence: 99%

Distributed Event‐Triggered Output Synchronization of Complex‐Valued Memristive Reaction‐Diffusion Complex Networks with Spatial Sampled‐Data

Chen

Cheng

2021

Complexity

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This study addresses the problem of output quasisynchronization for coupled complex-valued memristive reaction-diffusion complex networks via the distributed event-triggered control scheme. First, by using the separate method, set value mapping, and intermediate value theorem, the complex-valued memristive reaction-diffusion complex networks can be transferred into two semi-uncertain real-valued reaction-diffusion complex networks. Second, a distributed output piecewise event-triggered control (OPETC) scheme with spatial sampled-data is first proposed including a spatial sampling event-triggered generator and spatiotemporal sampling state feedback controller. Furthermore, this scheme can effectively save the measurement resources and lower the update rate of controllers in spatial and time domain. Third, the synchronization analysis is considered by utilizing an appropriate Lyapunov function, the Halanay inequality, and the improved Wirtinger inequality. Subsequently, several output event-triggered quasisynchronization criteria are derived. The relations among event trigger conditions, spatial sampling interval, convergence rate, and control gain are given by rigorous mathematical derivation. Finally, multiple simulations are compared to substantiate the validation of the OPETC scheme.

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Section: Remarkmentioning

confidence: 99%

Distributed Event‐Triggered Output Synchronization of Complex‐Valued Memristive Reaction‐Diffusion Complex Networks with Spatial Sampled‐Data

Chen

Cheng

2021

Complexity

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Section: Introductionmentioning

confidence: 99%

“…Recently, the event‐triggered control of PDE systems has received increasing attentions 1–3,12–22 . Particularly, the event‐triggered stabilization of hyperbolic and parabolic PDE systems is investigated in works 1,2,18–22 and works, 3,13–17 respectively. However, the systems therein all require the parameters to be exactly known, which greatly limits the application scope of the existing results.…”

Section: Introductionmentioning

confidence: 99%

“…We would like to highlight the contributions of this article in the following threefold: (i) The presence of unknown parameters makes the system under investigation essentially different from those in the related literature . In the existing works, 1–3,13–22 all the systems therein do not allow unknown system parameters, which makes the traditional control approaches cannot achieve the event‐triggered stabilization of system (1). In fact, to the authors' knowledge, the present article is the first attempt to consider the adaptive event‐triggered stabilization of distributed parameter systems with unknown parameters.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive event‐triggered control for a class of uncertain hyperbolic PDE‐ODE cascade systems

Liu

et al. 2021

Intl J Robust & Nonlinear

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This article investigates the event‐triggered stabilization for a class of hyperbolic PDE‐ODE cascade systems with nonlocal term. The presence of unknown parameters in the system brings technical challenges from design to analysis. This compels us to integrate certain powerful dynamic compensation into event‐triggering control mechanism. To solve the problem, by adaptive technique, a compensation strategy is developed to counteract the parametric uncertainties. Then, a desired event‐triggered controller is delicately designed to guarantee that all the signals in the closed‐loop system are bounded and the original system states converge to zero in the L2 norm. Particularly, the event‐triggering mechanism with an additional dynamic signal in the threshold is devised to overcome the negative influence of execution error, while ensuring a positive lower bound for the interexecution intervals. Finally, a simulation example is given to illustrate the effectiveness of the proposed control strategy.

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“…Adaptation of sampling periods in sampled-data systems is a topic close to event/self-triggered control, which has been also explored in [12] for finite-dimensional systems. Event-triggered control methods have been extended to some classes of infinite-dimensional systems, e.g., systems with output delays and packet losses [20], first-order hyperbolic systems [6,7], second-order hyperbolic systems [3], second-order parabolic systems [13,16,32], and abstract linear evolution equations [36]. However, relatively little work has been done on selftriggered control for infinite-dimensional systems, compared with event-triggered control.…”

mentioning

confidence: 99%

Stability analysis of infinite-dimensional event-triggered and self-triggered control systems with Lipschitz perturbations

Wakaiki¹,

Sano²

2022

MCRF

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This paper addresses the following question: "Suppose that a state-feedback controller stabilizes an infinite-dimensional linear continuoustime system. If we choose the parameters of an event/self-triggering mechanism appropriately, is the event/self-triggered control system stable under all sufficiently small nonlinear Lipschitz perturbations?" We assume that the stabilizing feedback operator is compact. This assumption is used to guarantee the strict positiveness of inter-event times and the existence of the mild solution of evolution equations with unbounded control operators. First, for the case where the control operator is bounded, we show that the answer to the above question is positive, giving a sufficient condition for exponential stability, which can be employed for the design of event/self-triggering mechanisms. Next, we investigate the case where the control operator is unbounded and prove that the answer is still positive for periodic event-triggering mechanisms.

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Event-triggered damping of a linear wave equation

Cited by 16 publications

References 19 publications

Distributed Event‐Triggered Output Synchronization of Complex‐Valued Memristive Reaction‐Diffusion Complex Networks with Spatial Sampled‐Data

Distributed Event‐Triggered Output Synchronization of Complex‐Valued Memristive Reaction‐Diffusion Complex Networks with Spatial Sampled‐Data

Adaptive event‐triggered control for a class of uncertain hyperbolic PDE‐ODE cascade systems

Stability analysis of infinite-dimensional event-triggered and self-triggered control systems with Lipschitz perturbations

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