Step size analysis in discrete-time dynamic average consensus

Montijano, Eduardo; Montijano, J. I.; Sagüés, Carlos; Martínez, Sònia

doi:10.1109/acc.2014.6859239

Cited by 10 publications

(4 citation statements)

References 15 publications

(33 reference statements)

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“…m times (a) Dynamic average consensus algorithm (32) in [66] where ∆ (m) = (1 − z −1 ) m is the m th divided difference (see also [67] for a stepsize analysis). The performance does not degrade when the graph is timevarying, but the estimate is delayed by m iterations.…”

Section: Signals With a Known Model (Discrete Time)mentioning

confidence: 99%

“…The estimate of the average, however, is delayed by m iterations due to the transfer function having a factor of z −m between the input and output. This problem is (32) in [66] where ∆ (m) = (1 − z −1 ) m is the m th divided difference (see also [67] for a stepsize analysis). The performance does not degrade when the graph is timevarying, but the estimate is delayed by m iterations.…”

Section: Signals With a Known Model (Discrete Time)mentioning

confidence: 99%

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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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Section: Signals With a Known Model (Discrete Time)mentioning

confidence: 99%

Section: Signals With a Known Model (Discrete Time)mentioning

confidence: 99%

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

et al. 2019

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“…That is, we design a distributed algorithm that steers a group of heterogeneous LTI followers to be at the sampled states of the leader at finite time just before the next sampled state is obtained. We note that practical one step lagged tracking has also been used in [26], [27], [28] for a set of dynamic average consensus algorithms with asymptotic tracking behavior. Our solution is inspired by the minimum energy controller design [29] in the classical optimal control theory, and is proposed for problems where the interaction topology of the followers plus the leader is an acyclic digraph with the leader as the global sink.…”

Section: Statement Of Contributionsmentioning

confidence: 99%

Distributed leader following of an active leader for linear heterogeneous multi-agent systems

Chung

Kia

2020

Systems & Control Letters

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This paper considers a leader-following problem for a group of heterogeneous linear time invariant (LTI) followers that are interacting over a directed acyclic graph. Only a subset of the followers has access to the state of the leader in specific sampling times. The dynamics of the leader that generates its sampled states is unknown to the followers. For interaction topologies in which the leader is a global sink in the graph, we propose a distributed algorithm that allows the followers to arrive at the sampled state of the leader by the time the next sample arrives. Our algorithm is a practical solution for a leader-following problem when there is no information available about the state of the leader except its instantaneous value at the sampling times. Our algorithm also allows the followers to track the sampled state of the leader with a locally chosen offset that can be time-varying. When the followers are mobile agents whose state or part of their state is their position vector, the offset mechanism can be used to enable the followers to form a transnational invariant formation about the sampled state of the leader. We prove that the control input of the followers to take them from one sampled state to the next one is minimum energy. We also show in case of the homogeneous followers, after the first sampling epoch the states and inputs of all the followers are synchronized with each other. Numerical examples demonstrate our results.

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“…Inspired by the idea of event-triggered control for multiagent systems [33], we consider the following event-triggered versions of the robust dynamic average consensus algorithm and the adaptive law given in (13) and (12), respectively:…”

Section: A Dynamic Event-triggered Algorithmmentioning

confidence: 99%

Distributed Robust Dynamic Average Consensus with Dynamic Event-Triggered Communication

George

Yang

2018

2018 IEEE Conference on Decision and Control (CDC)

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This paper presents the formulation and analysis of a fully distributed dynamic event-triggered communication based robust dynamic average consensus algorithm. Dynamic average consensus problem involves a networked set of agents estimating the time-varying average of dynamic reference signals locally available to individual agents. We propose an asymptotically stable solution to the dynamic average consensus problem that is robust to network disruptions. Since this robust algorithm requires continuous communication among agents, we introduce a novel dynamic event-triggered communication scheme to reduce the overall inter-agent communications. It is shown that the event-triggered algorithm is asymptotically stable and free of Zeno behavior. Numerical simulations are provided to illustrate the effectiveness of the proposed algorithm.

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Step size analysis in discrete-time dynamic average consensus

Cited by 10 publications

References 15 publications

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

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

Distributed leader following of an active leader for linear heterogeneous multi-agent systems

Distributed Robust Dynamic Average Consensus with Dynamic Event-Triggered Communication

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