Browse > Article
http://dx.doi.org/10.5302/J.ICROS.2013.13.9002

Discrete-Time State Feedback Algorithm for State Consensus of Uncertain Homogeneous Multi-Agent Systems  

Yoon, Moon-Chae (School of Electrical Engineering, Korea University)
Kim, Jung-Su (Dept. of Electrical and Information Engineering, Seoul National University of Science and Technology)
Back, Juhoon (School of Robotics, Kwangwoon University)
Publication Information
Journal of Institute of Control, Robotics and Systems / v.19, no.5, 2013 , pp. 390-397 More about this Journal
Abstract
This paper presents a consensus algorithm for uMAS (uncertain Multi-Agent Systems). Unlike previous results in which only nominal models for agents are considered, it is assumed that the uncertain agent model belongs to a known polytope set. In the middle of deriving the proposed algorithm, a convex set is found which includes all uncertainties in the problem using convexity of the polytope set. This set plays an important role in designing the consensus algorithm for uMAS. Based on the set, a consensus condition for uMAS is proposed and the corresponding consensus design problem is solved using LMI (Linear Matrix Inequality). Simulation result shows that the proposed consensus algorithm successfully leads to consensus of the state of uMAS.
Keywords
multi-agent system; state consensus; model uncertainties; state feedback; linear matrix inequality;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 J. A. Fax and R. M. Murray, "Information flow and cooperative control of vehicle formations," IEEE Transactions on Automatic Control, vol. 49, no. 9, pp. 1465-1476, 2004.   DOI   ScienceOn
2 P. Wieland, J.-S. Kim, and F. Allgower, "On topology and dynamics of consensus among linear high-order agents," International Journal of Systems Science, vol. 42, no. 10, pp. 1831-1842, 2011.   DOI   ScienceOn
3 J. Wang, D. Cheng, and X. Hu, "Consensus of multi-agent linear dynamic systems," Asian Journal of Control, vol. 10, pp. 144-155, 2008.   DOI   ScienceOn
4 J. Lee and J.-S. Kim, "Discrete time consensus problem using optimal control," ICROS-SICE International Joint. Conference, pp. 262-266, 2009.
5 S. E. Tuna, "LQR-based coupling gain for synchronization of linear systems," Arxiv:0801.3390, 2008.
6 J. Lee and J.-S. Kim, "Disc margins of the discrete-time LQR and its application to consensus problem," International Journal of Systems Science, vol. 43, no. 10, pp. 1891-1900, 2012.   DOI
7 J. H. Seo, H. Shim, and J. Back, "Consensus of high-order linear systems using dynamic output feedback compensator: low gain approach," IEEE Transactions on Automatica Control, vol. 11, pp. 2659-2664, 2009.
8 M. Darouach, M. Zasadzinski, and S. J. Xu, "Full-order observers for linear systems with unknown inputs," IEEE Transactions on Automatic Control, vol. 39, no. 3, pp. 606-609, 1994.   DOI   ScienceOn
9 P. Wieland and F. Allgower, "On consensus among identical linear systems using input-decoupled functional observers," Proc. of Amer. Control Conference, pp. 1641-1646, 2010.
10 P. Wieland, "From static to dynamic couplings in consensus and synchronization among identical and non-identical systems," Ph.D. Thesis, University of Stuttgart, 2010.
11 Reinhard Diestel, Graph Theory, 4th Ed., Springer-Verlag, 2010.
12 J. Lee, "Discrete-time consensus algorithms design using optimal control," Master Thesis, Seoul National University, 2010.
13 H. Kim, H. Shim, and J. Seo, "Output consensus of heterogeneous uncertain linear multi-agent systems," IEEE Transactions on Automatic Control, vol. 56, no. 1, pp. 200-206, 2011.   DOI   ScienceOn
14 P. Wieland, R. Sepulchre, and F. Allgower, "An internal model principle is necessary and sufficient for linear output synchronization," Automatica, vol. 47, pp. 1068-1074, 2011.   DOI   ScienceOn
15 J. Kim, J. Yang, H. Shim, and J.-S. Kim, "Synchronization of linear time-varying multi-agent systems with heterogeneous time-varying disturbances using integral controller," Journal of Institute of Control, Robotics and Systems (in Korean), vol. 18 no. 7, pp. 622-626, 2012.   과학기술학회마을   DOI   ScienceOn
16 M. Bazaraa, H. Sherali, and C. Shetty, Nonlinear Programming: Theory and Algorithms, 2nd Ed., WILEY, 1993.
17 S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadelphia: SIAM, 1994.
18 J. Kim, H. Kim, H. Shim, and J. Back, "Output consensus of non-identical and stabilizable linear systems having the same transfer matrix," Journal of Institute of Control, Robotics and Systems (in Korean), vol. 17 no. 9, pp. 851-953, 2011.   과학기술학회마을   DOI   ScienceOn