| Title: | Control a state-dependent dynamic graph to a pre-specified structure (English) | 
| Author: | Chen, Fei | 
| Author: | Chen, Zengqiang | 
| Author: | Liu, Zhongxin | 
| Author: | Yuan, Zhuzhi | 
| Language: | English | 
| Journal: | Kybernetika | 
| ISSN: | 0023-5954 | 
| Volume: | 45 | 
| Issue: | 5 | 
| Year: | 2009 | 
| Pages: | 801-808 | 
| Summary lang: | English | 
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| Category: | math | 
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| Summary: | Recent years have witnessed an increasing interest in coordinated control of distributed dynamic systems. In order to steer a distributed dynamic system to a desired state, it often becomes necessary to have a prior control over the graph which represents the coupling among interacting agents. In this paper, a simple but compelling model of distributed dynamical systems operating over a dynamic graph is considered. The structure of the graph is assumed to be relied on the underling system's states. Then by following a proper protocol, the state-dependent dynamic graph is driven to a pre-specified structure. The main results are derived via Lasalle's Invariant Principle and numerical examples that find very good agreements with the analytical results are also included. (English) | 
| Keyword: | state-dependent graph | 
| Keyword: | Lasalleś Invariant Principle | 
| Keyword: | dynamic system | 
| MSC: | 34D20 | 
| MSC: | 37F99 | 
| MSC: | 93D20 | 
| idZBL: | Zbl 1197.37061 | 
| idMR: | MR2599113 | 
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| Date available: | 2010-06-02T19:15:22Z | 
| Last updated: | 2012-06-06 | 
| Stable URL: | http://hdl.handle.net/10338.dmlcz/140044 | 
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| Reference: | [1] L. Conradt and T. J. Roper: Consensus decision making in animals.Trends Ecol. Evol. 20 (2005), 450–456. | 
| Reference: | [2] D. V. Dimarogonas and K. J. Kyriakopoulos: On the rendezvous problem for multiple nonholonomic agents.IEEE Trans. Automat. Control 52 (2007), 5, 916–922. MR 2324255 | 
| Reference: | [3] N. R. Franks, A. Dornhaus, J. P. Fitzsimmons, and M. Stevens: Speed versus accuracy in collective decision making.Proc. Roy. Soc. London Ser. B 270 (2003), 270, 2457–2463. | 
| Reference: | [4] Y. Hatano and M. Mesbahi: Agreement over random networks.IEEE Trans. Automat. Control 50 (2005), 11, 1867–1872. MR 2182742 | 
| Reference: | [5] A. Jadbabaie, J. Lin, and A. S. Morse: Coordination of groups of mobile autonomous agents using nearest neighbor rules.IEEE Trans. Automat. Control 48 (2003), 6, 988–1001. MR 1986266 | 
| Reference: | [6] S. J. Lu and L. Chen: A general synchronization method of chaotic communication systems via Kalman filtering.Kybernetika 44 (2008), 1, 43–52. MR 2405054 | 
| Reference: | [7] M. Mesbahi: On state-dependent dynamic graphs and their controllability properties.IEEE Trans. Automat. Control 50 (2005), 3, 387–392. MR 2123101 | 
| Reference: | [8] L. Moreau: Stability of multiagent systems with time-dependent communication links.IEEE Trans. Automat. Control 50 (2005), 2, 169–182. MR 2116423 | 
| Reference: | [9] T. Vicsek, A. Cziroäok, E. Ben-Jacob, I. Cohen, and O. Shochet: Novel type of phase transition in a system of self-deriven particles.Phys. Rev. Lett. 75 (1995), 6, 1226–1229. | 
| Reference: | [10] M. M. Zavlanos and G. J. Pappas: Controlling connectivity of dynamic graphs.In: IEEE Conf. on Decision and Control and European Control Conference, Seville 2005, p. 6. | 
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