Distributed Control for Multiagent Consensus Motions with Nonuniform Time Delays

Shi, Mengji; Qin, Kaiyu

doi:10.1155/2016/3567682

Cited by 9 publications

(12 citation statements)

References 23 publications

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“…Since the elements of the vector obtained by calculating the left part of (14) are equal to zero, it can be easy to obtain that (− ) 1 = 2 . Then, on the left side of (14), multiply by (the conjugate transpose of ); the following equation can be obtained:…”

Section: Theorem 4 Suppose That a Double-integrator Fomas Is Composementioning

confidence: 99%

“…In [13], the authors proposed a distributed protocol for consensus of second-order multiagent systems with inherent nonlinear dynamics and communication time delay. In [14], the authors solved control problems of agents achieving consensus motions in presence of nonuniform time delays. In [15], the authors investigated robust ∞ consensus control problems involving input delays for uncertain multiagent systems.…”

Section: Introductionmentioning

confidence: 99%

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Consensus of Fractional-Order Multiagent Systems with Double Integral and Time Delay

Liu

Chen

Qin

et al. 2018

Mathematical Problems in Engineering

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This paper is devoted to the consensus problems for a fractional-order multiagent system (FOMAS) with double integral and time delay, the dynamics of which are double-integrator fractional-order model, where there are two state variables in each agent. The consensus problems are investigated for two types of the double-integrator FOMAS with time delay: the double-integrator FOMAS with time delay whose network topology is undirected topology and the double-integrator FOMAS with time delay whose network topology is directed topology with a spanning tree in this paper. Based on graph theory, Laplace transform, and frequency-domain theory of the fractional-order operator, two maximum tolerable delays are obtained to ensure that the two types of the doubleintegrator FOMAS with time delay can asymptotically reach consensus. Furthermore, it is proven that the results are also suitable for integer-order dynamical model. Finally, the relationship between the speed of convergence and time delay is revealed, and simulation results are presented as a proof of concept.

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Section: Theorem 4 Suppose That a Double-integrator Fomas Is Composementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Consensus of Fractional-Order Multiagent Systems with Double Integral and Time Delay

Liu

Chen

Qin

et al. 2018

Mathematical Problems in Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

“…A control protocol based on distributed sampling data was proposed to achieve system consensus, but the delay condition was not taken into account in the algorithm. Reference [15] studied the consensus of second-order multi-robot systems under non-uniform and multi-time delays using the frequency domain analysis method. Compared with the Lyapunov method, it has lower conservativeness, and the results were extended to higher-order multi-robot systems.…”

Section: Introductionmentioning

confidence: 99%

Consensus Algorithms Based Multi-Robot Formation Control under Noise and Time Delay Conditions

Wei¹,

Lv²,

Duo³

et al. 2019

Applied Sciences

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In recent years, the formation control of multi-mobile robots has been widely investigated by researchers. With increasing numbers of robots in the formation, distributed formation control has become the development trend of multi-mobile robot formation control, and the consensus problem is the most basic problem in the distributed multi-mobile robot control algorithm. Therefore, it is very important to analyze the consensus of multi-mobile robot systems. There are already mature and sophisticated strategies solving the consensus problem in ideal environments. However, in practical applications, uncertain factors like communication noise, communication delay and measurement errors will still lead to many problems in multi-robot formation control. In this paper, the consensus problem of second-order multi-robot systems with multiple time delays and noises is analyzed. The characteristic equation of the system is transformed into a quadratic polynomial of pure imaginary eigenvalues using the frequency domain analysis method, and then the critical stability state of the maximum time delay under noisy conditions is obtained. When all robot delays are less than the maximum time delay, the system can be stabilized and achieve consensus. Compared with the traditional Lyapunov method, this algorithm has lower conservativeness, and it is easier to extend the results to higher-order multi-robot systems. Finally, the results are verified by numerical simulation using MATLAB/Simulink. At the same time, a multi-mobile robot platform is built, and the proposed algorithm is applied to an actual multi-robot system. The experimental results show that the proposed algorithm is finally able to achieve the consensus of the second-order multi-robot system under delay and noise interference.

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“…In the past decade, research results have been continuously springing up about consensus problems of various multiagent systems. Examples include consensus problems of multiagent systems with different dynamics such as first-order dynamics in [4], second-order dynamics in [5], and high-order dynamics in [6]; consensus problems of multiagent systems with different time delays such as fixed time delays in [7], time-varying delays in [8], and multiple time delays in [9]; and consensus problems of multiagent systems with different network topologies such as fixed topology in [10], switching topology in [11], and randomly switching topology in [12].…”

Section: Introductionmentioning

confidence: 99%

Consensus of Fractional-Order Multiagent Systems with Nonuniform Time Delays

Liu

Qin

Chen

et al. 2018

Mathematical Problems in Engineering

Self Cite

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Due to the complex external environment, many multiagent systems cannot be precisely described or even cannot be described by an integer-order dynamical model and can only be described by a fractional-order dynamical model. In this paper, consensus problems are investigated for two types of fractional-order multiagent systems (FOMASs) with nonuniform time delays: FOMAS with symmetric time delays and undirected topology and FOMAS with asymmetric time delays and directed topology. Employing the Laplace transform and the frequency-domain theory, two delay margins are obtained to guarantee the consensus for the two types of FOMAS, respectively. These results are also suitable for the integer-order dynamical model. Finally, simulation results are provided to illustrate the effectiveness of our theoretical results.

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Distributed Control for Multiagent Consensus Motions with Nonuniform Time Delays

Cited by 9 publications

References 23 publications

Consensus of Fractional-Order Multiagent Systems with Double Integral and Time Delay

Consensus of Fractional-Order Multiagent Systems with Double Integral and Time Delay

Consensus Algorithms Based Multi-Robot Formation Control under Noise and Time Delay Conditions

Consensus of Fractional-Order Multiagent Systems with Nonuniform Time Delays

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