Leaderless Consensus of Non-linear Mixed delay Multi-agent Systems with Random Packet Losses via Sampled-data Control

Abstract

This paper inspects the consensus problem of nonlinear mixed delay multi-agent systems with random packet losses through the sampled-data control using the undirected graph without any specified leader for the other following agents. The probabilistic time varying delay is taken in the control input delay that Bernoulli distributed white sequence is engaged to formulate the random packet losses between the agents. The consensus problem can be changed over into a stabilization problem by using the Laplacian matrix which can be obtained by undirected graph. By framing a Lyapunov-Krasovskii functional with triple integral terms and implementation of the property of Kronecker product together with some well known matrix inequality techniques, a mean square consensus for mixed delay multi-agent system can be achieved. Terminally, two numerical examples are provided to illuminate the advantages of the suggested techniques.

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Correspondence to M. Syed Ali.

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Recommended by Editor Jessie (Ju H.) Park. This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant No. (DF-518-130-1441). The authors, therefore, gratefully acknowledge DSR technical and financial support.

M. Syed Ali is working as an Assistant Professor in Department of Mathematics, Thiruvalluvar University, Vellore, Tamil Nadu, India. He was awarded Young Scientist Award 2016 by the Academy of Sciences, Chennai. He has published more than 140 research papers in various SCI journals holding impact factors. He has also published research articles in national journals and international conference proceedings. He also serves as a reviewer for several SCI journals. His research interests include stochastic differential equations, dynamical systems, complex networks.

R. Agalya is pursuing a Ph.D. degree in the Department of Mathematics, Thiruvalluvar University, Tamil Nadu, India. Her research interests are genetic regulatory networks, Neural networks, Multi-agent system.

Sumit Saroha is with Department of Printing Technology (Electriacal Engineering), Guru Jhambheswar university of Science and Tecchnology, Hisar, India. His research interests includes fractional order systems and Multi agent systems.

Tareq Saeed received his B.S. degrees in Mathematics from King Abdulaziz, Jeddah, Saudi Arabia, his M.S. degree in Financial Mathematics from Wollongong University, and a Ph.D. degree in Griffith University, in 2018. Currently, He is working as an Assistant Professor at the Mathematics Department, King Abdulaziz University (KAU).

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Syed Ali, M., Agalya, R., Saroha, S. et al. Leaderless Consensus of Non-linear Mixed delay Multi-agent Systems with Random Packet Losses via Sampled-data Control. Int. J. Control Autom. Syst. 18, 1885–1893 (2020). https://doi.org/10.1007/s12555-019-0446-1

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Keywords

  • Consensus
  • Kronecker product
  • multi-agent systems (MASs)
  • probabilistic time delay