Synchronization in networks of linear agents with output feedbacks
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The problem is considered of asymptotic synchronization by states in networks of identical linear agents in the application of the consensual output feedback. For the networks with fixed topology and without delay in the information transmission, on the basis of the passification theorem and the Agaev-Chebotarev theorem, the possibility is established of the provision of synchronization (consensus) of strong feedback under the assumption of the strict passification of agents and the existence of the incoming spanning tree in the information graph. In contrast to the known works, in which only the problems with the number of controls equal to the number of variables of the state of agents are investigated, in this work a substantially more complex case is considered, where the number of controls is less than the number of variables of the state, namely: the control is scalar. The results are illustrated by the example for the ring-shaped network of four dual integrators.
KeywordsRemote Control Span Tree Multiagent System Network Control System Laplace Matrix
- 6.IEEE Trans. Autom. Control, Special Issue on Networked Control Systems, September 2004.Google Scholar
- 7.IEEE Control Syst. Mag., Special Section “Complex Networked Control Systems,” August 2007.Google Scholar
- 8.Proc. IEEE, Special Issue on Networked Control Systems Technology, January 2007.Google Scholar
- 9.Proc. 1st IFAC Workshop on Estimation and Control of Networked Systems, September 24–26, 2009, Venice, http://www.ifac-papersonline.net/.
- 10.Proc. 2nd IFAC Workshop on Estimation and Control of Networked Systems, September 13–14, 2010, Grenoble, http://www.ifac-papersonline.net/.
- 11.Chebotarev, P.Yu. and Agaev, R.P., Coordination in Multiagent Systems and Laplacian Spectra of Digraphs, Autom. Remote Control, 2009, no. 3, pp. 469–483.Google Scholar
- 13.Mohar, B., Some Applications of Laplace Eigenvalues of Graphs: Graph Symmetry: Algebraic Methods and Applications, NATO ASI Ser. C 497, 1997, pp. 225–275.Google Scholar
- 14.Agaev, R.P. and Chebotarev, P.Yu., Laplace Spectra of Orgraphs and Their Applications, Autom. Remote Control, 2005, no. 5, pp. 719–733.Google Scholar
- 19.Yoshioka, C. and Namerikawa, T., Observer-Based Consensus Control Strategy for Multiagent System with Communication Time Delay, Proc. IEEE MSC-2008, San-Antonio, 2008, pp. 1037–1042.Google Scholar
- 21.Agaev, R.P. and Chebotarev, P.Yu., The Matrix of Maximum Out Forests of a Digraph and Its Applications, Autom. Remote Control, 2000, no. 9, pp. 1424–1450.Google Scholar
- 22.Agaev, R.P. and Chebotarev, P.Yu., Spanning Forests of a Digraph and Their Applications, Autom. Remote Control, 2001, no. 3, pp. 443–466.Google Scholar
- 23.Fradkov, A.L., Quadratic Lyapunov Functions in the Problem of Adaptive Stabilization of a Linear Dynamic Object, Sib. Mat. Zh., 1976, no. 2, pp. 436–446.Google Scholar
- 24.Fradkov, A.L., Passification of Nonsquare Linear Systems and Feedback Yakubovich-Kalman-Popov Lemma, Eur. J. Control, 2003, no. 6, pp. 573–582.Google Scholar
- 26.Polyshin, I.G., Fradkov, A.L., and Hill, D.J., Passivity and Passification of Nonlinear Systems, Autom. Remote Control, 2000, no. 3, pp. 355–388.Google Scholar
- 28.Andrievskii, B.R. and Fradkov, A.L., Method of Passification in Adaptive Control, Estimation, and Synchronization, Autom. Remote Control, 2006, no. 11, pp. 1699–1731.Google Scholar
- 29.Fradkov, A.L., Kiberneticheskaya fizika: printsipy i primery (Cybernetic Physics: Principle and Examples), St. Petersburg: Nauka, 2003.Google Scholar
- 32.Marcus, M. and Minc, H., A Servey of Matrix Theory and Matrix Inequalities, Boston: Allyn and Bacon, 1964. Translated under the title Obzor po teorii matrits i matrichnykh neravenstv, Moscow: Nauka, 1972.Google Scholar