Discussion about Sliding Mode Algorithms, Zeno Phenomena and Observability

Yu, Lei; Barbot, Jean‐Pierre; Benmerzouk, Djamila; Boutat, Driss; Floquet, Thierry; Zheng, Gang

doi:10.1007/978-3-642-22164-4_7

Cited by 5 publications

(2 citation statements)

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“…As a further result, a lower bound for the time elapsed between consecutive triggering events is provided in the paper, which excludes the existence of an accumulation point, i.e. the notorious Zeno phenomenon, also known as 'Fuller phenomenon' (see Liberzon, 2003) and long recognised in sliding mode theory (Ames, Tabuada, & Sastry, 2006;Johansson, Lygeros, Sastry, & Egerstedt, 1999;Yu et al, 2012). All the paper results have been proved in spite of the possible presence of transmission delays.…”

Section: Introductionmentioning

confidence: 71%

Event-triggered variable structure control

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Incremona

Ferrara

2019

International Journal of Control

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This paper presents a novel variable structure control (VSC) algorithm of event-triggered (ET) type, capable of dealing with a class of nonlinear uncertain systems. By virtue of its ET nature, the algorithm can be used as the kernel of a robust networked control system. The design objective is indeed to reduce the number of transmissions over the network. The proposed ET-VSC also guarantees appropriate robustness properties, even in the presence of delayed transmissions. It is theoretically analysed, proving that the sliding variable associated with the controlled system results in being ultimately confined into a boundary layer of prescribed amplitude. As a consequence, it is proved that the state of the considered uncertain nonlinear system is ultimately bounded as well. Moreover, a lower bound for the time elapsed between consecutive triggering events is provided, which excludes the notorious Zeno behaviour. Finally, the designed ET-VSC control scheme is satisfactorily assessed in simulation. ARTICLE HISTORY

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Section: Introductionmentioning

confidence: 71%

Event-triggered variable structure control

Cucuzzella

Incremona

Ferrara

2019

International Journal of Control

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“…The reader may also recall that commutations at infinite frequency between two subsystems is termed as the Zeno phenomenon in the literature of hybrid systems. The interested reader can find an enlightening discussion on the relation between first-order sliding mode chattering and Zeno phenomenon in [74]. From a practical perspective, chattering is undesirable and leads to excessive control energy expenditure [75].…”

Section: Sidebar: Euler Discretizations Of Continuous-time Dynamic Av...mentioning

confidence: 99%

Tutorial on Dynamic Average Consensus: The Problem, Its Applications, and the Algorithms

et al. 2019

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Technological advances in ad-hoc networking and the availability of low-cost reliable computing, data storage and sensing devices have made possible scenarios where the coordination of many subsystems extends the range of human capabilities. Smart grid operations, smart transportation, smart healthcare and sensing networks for environmental monitoring and exploration in hazardous situations are just a few examples of such network operations. In these applications, the ability of a network system to, in a decentralized fashion, fuse information, compute common estimates of unknown quantities, and agree on a common view of the world is critical. These problems can be formulated as agreement problems on linear combinations of dynamically changing reference signals or local parameters. This dynamic agreement problem corresponds to dynamic average consensus, which is the problem of interest of this article. The dynamic average consensus problem is for a group of agents to cooperate in order to track the average of locally available time-varying reference signals, where each agent is only capable of local computations and communicating with local neighbors, see Figure 1. Figure 1: A group of communication agents, each endowed with a time-varying reference signal. 1 arXiv:1803.04628v2 [cs.SY] 24 Nov 2018 Centralized solutions have drawbacksThe difficulty in the dynamic average consensus problem is that the information is distributed across the network. A straightforward solution, termed centralized, to the dynamic average consensus problem appears to be to gather all of the information in a single place, do the computation (in other words, calculate the average), and then send the solution back through the network to each agent. Although simple, the centralized approach has numerous drawbacks: (1) the algorithm is not robust to failures of the centralized agent (if the centralized agent fails, then the entire computation fails), (2) the method is not scalable since the amount of communication and memory required on each agent scales with the size of the network, (3) each agent must have a unique identifier (so that the centralized agent counts each value only once), (4) the calculated average is delayed by an amount which grows with the size of the network, and (5) the reference signals from each agent are exposed over the entire network which is unacceptable in applications involving sensitive data. The centralized solution is fragile due to existence of a single failure point in the network. This can be overcome by having every agent act as the centralized agent. In this approach, referred to as flooding, agents transmit the values of the reference signals across the entire network until each agent knows each reference signal. This may be summarized as "first do all communications, then do all computations". While flooding fixes the issue of robustness to agent failures, it is still subject to many of the drawbacks of the centralized solution. Also, although this approach works reasonably well for small size networks,...

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Advantages of the usage of the Infinity Computer for reducing the Zeno behavior in hybrid system models

et al. 2022

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To capture the dynamics of modern Cyber-Physical Systems, hybrid system models are introduced to combine their continuous dynamics with the discrete ones. Unfortunately, one important negative issue can affect hybrid system models: the so-called Zeno phenomenon, which results in an infinite number of discrete transitions in a finite amount of time occurring during the model’s simulation that leads to inconsistent results. In this context, the paper investigates the use of a recently proposed numerical algorithm, based on the Infinity Computer methodology, to handle the Zeno phenomenon and evaluate it with respect to standard numerical methods by considering the hybrid system models of two exemplary Cyber-Physical Systems: the Water tanks and the Thermostat.

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Discussion about Sliding Mode Algorithms, Zeno Phenomena and Observability

Cited by 5 publications

References 32 publications

Event-triggered variable structure control

Event-triggered variable structure control

Tutorial on Dynamic Average Consensus: The Problem, Its Applications, and the Algorithms

Advantages of the usage of the Infinity Computer for reducing the Zeno behavior in hybrid system models

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