Structural Consensus Controllability of Singular Multi-Agent Linear Dynamic Systems

AUTHOR(S):

TITLE

Structural Consensus Controllability of Singular Multi-Agent Linear Dynamic Systems

ABSTRACT

The analysis of control of linear multi-agent systems has recently emerged as an important domain that is receiving a lot of interest from a variety of research communities, and consensus plays a fundamental role in this field of study. We will show how using linear algebra techniques can be analyzed the consensus controllability problem for singular multi-agent systems, in which all agents have an identical linear dynamic mode that can be in any order.

KEYWORDS

Singular multi-agent systems, consensus, controllability, Structural consensus controllability

REFERENCES

[1] Arnold, V.I., On matrices depending on parameters. UspekhiMat. Nauk.26, 1971. [1] Arnold, V.I., On matrices depending on parameters. UspekhiMat. Nauk.26, 1971.

[2] C.T. Chen, “Introduction to Linear System Theory”. Holt, Rinehart and Winston Inc, New York, (1970).

[3] L. Dai “Singular Control Systems”. Springer Verlag. New York (1989).

[4] A. Fax, R. Murray, Information flow and cooperative control of vehicle formations, IEEE Trans. Automat. Control. 49, (9), pp. 1453-1464, (2004).

[5] M.I. Garc´ıa-Planas, Sensivity and stability of singular systems under proportional and derivative feedback, Wseas Transactions on Mathematics, 8, (11), pp 635-644, (2009).

[6] M.I. Garc´ıa-Planas, Obtaining Consensus of Multi-agent Linear Dynamic Systems, Advances in Applied and Pure Mathematics, pp. 91-95, (2014)

[7] M.I. Garc´ıa-Planas, M.D. Magret, Miniversal deformations of linear systems under the full group action. Systems and control letters, 35, pp. 279–286, (1998).

[8] M.I. Garc´ıa-Planas, S. Tarragona, A. Diaz, Controllability of time-invariant singular linear systems. From physics to control through an emergent view. pp. 112 -117. World Scientific, 2010.

[9] A. Jadbabaie, J. Lin, A.S. Morse, Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Transaction on Automatic Control. 48 (6), pp. 943-948, (2007).

[10] P. Lancaster, M. Tismenetsky, “The Thoery of Matrices”. Academic Press. San Diego (1985).

[11] C.T. Lin, Structural Controllability. IEEE Trans. Automatic Control. AC-19, pp. 201–208, (1974).

[12] R.O. Saber, R.M. Murray, Consensus Protocols for Networks of Dynamic Agents, Report.

[13] R.O. Saber, R.M. Murray, Consensus problems in networks of agents with switching topology and time-delays, IEEE Trans. Automat. Control. 49, (9), pp. 1520-1533, (2004).

[14] J. Wang, D. Cheng, X. Hu, Consensus of multiagent linear dynamics systems, Asian Journal of Control 10, (2), pp. 144-155, (2008).

[15] D. West “Introduction to Graph Theory” Prentice Hall (3rd Edition), (2007).

[16] G. Xie, L. Wang, Consensus control for a class of networks of dynamic agents: switching topology, Proc. 2006 Amer. Contro. Conf., pp. 1382- 1387, (2007).

Cite this paper

M. Isabel García-Planas. (2016) Structural Consensus Controllability of Singular Multi-Agent Linear Dynamic Systems. Mathematical and Computational Methods, 1, 294-299