CONSENSUS ANALYSIS AND DESIGN OF LINEAR INTERCONNECTED MULTI-AGENT SYSTEMS

doi:10.1016/S0252-9602(15)30055-2

Acta mathematica scientia,Series B ›› 2015, Vol. 35 ›› Issue (6): 1305-1317.doi: 10.1016/S0252-9602(15)30055-2

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CONSENSUS ANALYSIS AND DESIGN OF LINEAR INTERCONNECTED MULTI-AGENT SYSTEMS

Yangzhou CHEN¹, Wei LI^2,3, Guiping DAI², A.Yu. ALEKSANDROV⁴

1. College of Metropolitan Transportation§Beijing Laboratory For Urban Mass Transit, Beijing University of Technology, Beijing 100124, China;
2. College of Metropolitan Transportation§Beijing University of Technology, Beijing 100124, China;
3. Department of Electromechanical Engineering, Shijiazhuang Institute of Railway Technology, Shijiazhuang 050041, China;
4. Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, St. Petersburg, Russia

Received:2015-05-18 Revised:2015-01-12 Online:2015-11-01 Published:2015-11-01
Supported by:
This work was supported in part by NSF of China (61273006 and 6141101096), High Technology Research and Development Program of China (863 Program) (2011AA110301), Specialized Research Fund for the Doctoral Program of Higher Education of China(20111103110017), St. Petersburg State University (9.38.674.2013) and the Russian Foundation for Basic Research (13-01-00376-a and 15-58-53017).

Abstract

Abstract:

We deal with the state consensus problem of a general Linear Interconnected Multi-Agent System (LIMAS) under a time-invariant and directed communication topology. Firstly, we propose a linear consensus protocol in a general form, which consists of state feedback of the agent itself and feedback form of the relative states between the agent and its neighbors. Secondly, a state-linear-transformation is applied to equivalently transform the state consensus problem into a partial stability problem. Based on the partial stability theory, we derive a sufficient and necessary criterion of consensus convergence, which is expressed via the Hurwitz stability of a real matrix constructed from the parameters of the agent models and the protocols, and present an analytical formula of the consensus function. Lastly, we propose a design procedure of the gain matrices in the protocol by solving a bilinear matrix inequality.

Key words: linear interconnected multi-agent system (LIMAS), partial stability, state-linear-transformation, criterion of consensus convergence, consensus design

CLC Number:

34D06

Yangzhou CHEN, Wei LI, Guiping DAI, A.Yu. ALEKSANDROV. CONSENSUS ANALYSIS AND DESIGN OF LINEAR INTERCONNECTED MULTI-AGENT SYSTEMS[J].Acta mathematica scientia,Series B, 2015, 35(6): 1305-1317.

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References

[1] Napoli M, Bamieh B. Modeling and observer design for an array of electrostatically actuated microcantilevers. Proceedings of the 40th IEEE Conference on Decision and Control, 2001: 4274-4279
[2] Venkat A N, Hiskens I A, Rawlings J B, et al. Distributed output feedback MPC for power system control. Proceedings of the 45th IEEE Conference on Decision and Control. 2006: 4038-4045
[3] Omony J, de Graaff L H, van Straten G, et al. Modeling and analysis of the dynamic behavior of the XlnR regulon in Aspergillus niger. BMC systems biology, 2011, 5(Suppl 1): S14
[4] Bragalli C, D'Ambrosio C, Lee J, et al. Case Studies in Operations Research. New York: Springer, 2015, 212: 183-198
[5] Han X G, Chen Y Z, Shi J J, et al. An extended cell transmission model based on digraph for urban traffic road network. Proceedings of the 15th IEEE Conference on Intelligent Transportation Systems, 2012: 558-563
[6] Yang T C. Networked control system: a brief survey. IEE Proceedings-Control Theory and Applications, 2006, 153(4): 403-412
[7] Heemels W, van de Wouw N. Networked Control Systems. London:Springer, 2010: 203-253
[8] Shang Y. Consensus formation of two-level opinion dynamics. Acta Mathematica Scientia, 2014, 34B(4): 1029-1040
[9] Guo W, Xiao H, Chen S. Consensus of the second-order multi-agent systems with an active leader and coupling time delay. Acta Mathematica Scientia, 2014, 34B(2): 453-465
[10] Olfati-Saber R, Fax J A, Murray R M. Consensus and cooperation in networked multi-agent systems. Proceedings of the IEEE, 2007, 95(1): 215-233
[11] Ren W, Cao Y. Distributed Coordination of Multi-agent Networks: Emergent Problems, Models, and Issues. London: Springer, 2010
[12] Scardovi L, Arcak M, Sontag E D. Synchronization of interconnected systems with applications to biochemical networks: An input-output approach. IEEE Transactions on Automatic Control, 2010, 55(6): 1367-1379
[13] Liu T, Hill D J, Zhao J. Incremental-dissipativity-based synchronization of interconnected systems. Proceedings of the 18th IFAC World Congress, 2011: 8890-8895
[14] Franci A, Scardovi L, Chaillet A. An Input-Output approach to the robust synchronization of dynamical systems with an application to the Hindmarsh-Rose neuronal model. Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference, 2011: 6504-6509
[15] Fradkov A, Junussov I, Ortega R. Decentralized adaptive synchronization in nonlinear dynamical networks with nonidentical nodes. Proceedings of the 2009 IEEE International Symposium on Control Applications and Intelligent Control, 2009: 531-536
[16] Lee S J, Oh K K, Ahn H S. Passivity-based output synchronisation of port-controlled Hamiltonian and general linear interconnected systems. IET Control Theory and Applications, 2013, 7(2): 234-245
[17] Lee S J, Ahn H. Passivity-based output synchronization of interconnected linear systems. Proceedings of the IEEE/ASME International Conference on Mechatronics and Embedded Systems and Applications, 2012: 46-51
[18] Russo G. Analysis, Control and synchronization of nonlinear systems and networks via Contraction Theory: theory and applications. Universita degli studi di Napoli Federico II, 2010
[19] Furtat I, Fradkov A, Tsykunov A. Robust synchronization of linear dynamical networks with compensation of disturbances. International Journal of Robust and Nonlinear Control, 2014, 24(17): 2774-2784
[20] Cheng Y, Ugrinovskii V A. Guaranteed performance leader-follower control for multi-agent systems with linear IQC coupling. Proceedings of the 2013 IEEE conference on American Control Conference, 2013: 2625-2630
[21] Ge Y R, Chen Y Z, Zhang Y X, et al. State consensus analysis and design for high-order discrete-time linear multiagent systems. Mathematical Problems in Engineering, 2013: Art ID192351
[22] Chen Y Z, Ge Y R, Zhang Y X. Partial stability approach to consensus problem of linear multi-agent systems. Acta Automatica Sinica, 2014, 40(11): 2573-2584
[23] Vorotnikov V I. Partial Stability and Control. Boston: Springer, 1998
[24] Wang Y G. BMI-based output feedback control design with sector pole assignment. Acta Automatica Sinica, 2008, 34(9): 1192-1195
[25] Fukuda M, Kojima M. Branch-and-cut algorithms for the bilinear matrix inequality eigenvalue problem. Comput Opt Appl, 2001, 19(1): 79-105
[26] Shimomura T, Fujii T. Multiobjective control via successive over-bounding of quadratic terms. International Journal of Robust and Nonlinear Control, 2005, 15(8): 363-381

CONSENSUS ANALYSIS AND DESIGN OF LINEAR INTERCONNECTED MULTI-AGENT SYSTEMS

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