Delay Consensus Margin of First-Order Multiagent Systems With Undirected Graphs and PD Protocols

Ma, Dan; Chen, Jianqi; Lu, Renquan; Chen, Jie; Chai, Tianyou

doi:10.1109/tac.2020.3035556

Cited by 29 publications

(21 citation statements)

References 22 publications

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“…On the other hand, determining the exact DCM poses a problem of significant challenge, and the generalities alluded to will render the problem hardly tractable, both technically and computationally. In this vein, we note that the generalization of first‐order results in Reference 15 to second‐order MASs is itself a nontrivial extension. While in the former case the DCM problem enjoys desirable monotonicity and smoothness properties and hence a variety of elementary tools can be used, for second‐order MASs these properties are no longer existent.…”

Section: Introductionmentioning

confidence: 93%

“…The DCM problem dwells on finding the maximal range of delay values allowable to achieve and maintain consensus. Recent works in DCM include, for example, References 14 and 15, which attempt to determine the DCM for MASs subject to unknown and uncertain delays. Specifically, for first‐order MASs with static, proportional feedback protocol, an analytical expression of the DCM was obtained in Reference 8.…”

Section: Introductionmentioning

confidence: 99%

“…Specifically, for first‐order MASs with static, proportional feedback protocol, an analytical expression of the DCM was obtained in Reference 8. It was found in Reference 15, however, that when employing more sophisticated consensus protocols, such as proportional‐derivative (PD) protocols, it is no longer possible to determine the DCM analytically; instead, the DCM was found to be computable by solving a smooth unimodal problem, which amounts to a univariate convex optimization problem. Yet as expected, the DCM problem becomes significantly more challenging for second‐order MASs.…”

Section: Introductionmentioning

confidence: 99%

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Exact computation of maximal allowable delay for general second‐order multi‐agents consensus

Chen

Chai

2021

Intl J Robust & Nonlinear

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The delay consensus margin (DCM) defines the largest delay range within which a distributed feedback control protocol can achieve and maintain the consensus robustly against uncertain time delays. This article investigates the exact computation of the DCM for general second-order multi-agent systems (MASs) under distributed proportional-derivative (PD) feedback, or alternatively known as position and velocity feedback protocols over undirected graphs. We consider MASs with uncertain constant delays, and derive the DCM expression for second-order agents and show that it can be determined by solving a non-smooth quasi-concave optimization problem. The DCM as such, can be computed via convex optimization methods.

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Section: Introductionmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Exact computation of maximal allowable delay for general second‐order multi‐agents consensus

Chen

Chai

2021

Intl J Robust & Nonlinear

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“…For its recognized advantages, there has been sustained interest in PID control. Some of the recent work on PID control has been focused on analytical studies, which have led to new findings, improved design and tuning rules on e.g., time delay systems, nonlinear systems, and extensions to multi-agent systems (Xu et al, 2013;Ma et al, 2020b). Specifically, steady-state tracking performance was examined in Åström and Hägglund (1995); Silva et al (2002), the delay robustness problems were studied in Silva et al (2002); Ma and Chen (2019); Chen et al (2019), and nonlinear regulation problems were considered in Zhao and Guo (2017).…”

Section: Introductionmentioning

confidence: 99%

PID control design for first-order delay systems via MID pole placement: Performance vs. robustness

Boussaada

Chen

et al. 2022

Automatica

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The PID control is favored in controlling industrial processes for its ease of implementation. In this paper we present an analytical study, with an aim at stability robustness, tracking performance, and pole placement of first-order unstable plants under PID control. We employ a multiplicity-induced dominancy (MID) strategy to design and tune PID controller gains, which is shown to possess desirable properties that ensure specified decay rate of the closed-loop response and the stability robustness of the closed-loop system in spite of variations in the delay parameter. We also study the tradeoff between delay robustness and tracking performance of PID controllers. We show that under the constraint of steady-state tracking, the maximal delay robustness range can be computed by solving a unimodal pseudo-concave optimization problem.

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“…For first-order multi-agent systems under undirected graph topology, Ref. [7] derives the analytical expression for the input delay margin by solving a univariate convex optimization problem. Similarly, the delay margins for a general second-order and double integrator multi-agent systems with communication delay under directed graph topology are deduced in Ref.…”

Section: Introductionmentioning

confidence: 99%

Consensus Control of Linear Multi-Agent Systems with Non-uniform Time-varying Communication Delays

Bhusal,

Subbarao

2020

Preprint

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This paper is concerned with the consensus problem for multi-agent systems subject to communication delays between the neighboring agents. We consider a scenario where each agent is characterized by a general high-order linear system and the communication delays between the agents are non-uniform and time-varying. We design a distributed control protocol for the agents and provide an equivalent stability problem to be solved that guarantees the state consensus in the group of agents. Moreover, a delay-dependent stability criterion is provided by combining the Lyapunov-Krasovskii method with the linear matrix inequality approach.

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Delay Consensus Margin of First-Order Multiagent Systems With Undirected Graphs and PD Protocols

Cited by 29 publications

References 22 publications

Exact computation of maximal allowable delay for general second‐order multi‐agents consensus

Exact computation of maximal allowable delay for general second‐order multi‐agents consensus

PID control design for first-order delay systems via MID pole placement: Performance vs. robustness

Consensus Control of Linear Multi-Agent Systems with Non-uniform Time-varying Communication Delays

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