A type of new consensus protocol for two-dimension multi-agent systems

Yibo Zhang; Jinfeng Gao; Jia Ren; Huijiao Wang

doi:10.3934/naco.2017022

Article Contents

2017, Volume 7, Issue 3: 345-357. Doi: 10.3934/naco.2017022

This issue Previous Article Analysis of optimal boundary control for a three-dimensional reaction-diffusion system Next Article A multistage stochastic programming framework for cardinality constrained portfolio optimization

A type of new consensus protocol for two-dimension multi-agent systems

Institute of Automation, Faculty of Mechanical Engineering and Automation, Zhejiang Sci-Tech University, Hangzhou 310018, P. R. China

* Corresponding author: Zhang Yibo
* Corresponding author: Zhang Yibo

The reviewing process of the paper was handled by Nanjing Huang as Guest Editors

Received: January 2016

Revised: June 2017

Published: October 2017

This work is supported by the National Natural Science Foundation of China (No. 61374083,61473264), Zhejiang Province Key Project of Science and Technology(No. 2014C03027), and Zhejiang Provincial Natural Science Foundation of China (No. LZ17F030002, LY17F030024).

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Abstract

A type of new consensus protocol for a two-dimension multi-agent system (MAS) is proposed. By introducing the conventional MAS and protocol, a dynamic equation of the first-order two-dimension MAS is proposed. then a new protocol with its Laplacian matrix is adopted. According to two types possible roots of character equations, two lemmas are proposed to show consensus asymptotical conditions. Furthermore, the convergence conditions of parameters are analyzed. Several simulated examples illustrate that consensus is achieved if the convergence conditions are satisfied.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3513A.

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Figure 1. All possible of multiple results of $\bar{\mu} _{i\pm }$

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Figure 2. A digraph without leaders

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Figure 3. Simulation results 1 of condition (1) in Lemma 1

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Figure 4. Simulation results 2 of condition (1) in Lemma 1

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Figure 5. Simulation results 1 of condition (2) in Lemma 1

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Figure 6. Simulation results 2 of condition (2) in Lemma 1

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Figure 7. Simulation results 2 of condition (3) in Lemma 1

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Figure 8. Simulation results of condition (3) in Lemma 1

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Figure 9. Simulation results of condition (3) in Lemma 1

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Figure 10. Simulation results 1 of condition (1) in Lemma 2

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Figure 11. Simulation results 2 of condition (1) in Lemma 2

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Figure 12. Simulation results 1 of condition (2) in Lemma 2

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Figure 13. Simulation results 1 of condition (2) in Lemma 2

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Figure 14. Simulation results if Lemma 1 is not hold

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Figure 15. Simulation results if Lemma 2 is not hold

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