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On the controllability and stabilizability of non-homogeneous multi-agent dynamical systems. (English) Zbl 1250.93033
Summary: In this paper, we consider a supervisory control scheme for non-homogenous multi-agent systems. Each agent is modeled through an independent strictly proper SISO state space model, and the supervisory controller, representing the information exchange among the agents, is implemented in turn via a linear state-space model. Controllability and observability of the overall system are characterized, and some preliminary results about stability and stabilizability are provided. The paper extends some of the results obtained in Hara et al. (2007, 2009) to non-homogenous multi-agent systems, and also for the homogeneous case.

MSC:
93B05 Controllability
93D21 Adaptive or robust stabilization
93A13 Hierarchical systems
93A14 Decentralized systems
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[1] Fax, J.A.; Murray, R.M., Information flow and cooperative control of vehicle formations, IEEE trans. automat. control, 49, 1465-1476, (2004) · Zbl 1365.90056
[2] Jadbabaie, A.; Lin, J.; Morse, A.S., Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE trans. automat. control, 48, 988-1001, (2003) · Zbl 1364.93514
[3] Olfati-Saber, R.; Fax, J.A.; Murray, R.M., Consensus and cooperation in networked multi-agent systems, Proc. IEEE, 95, 215-233, (2007) · Zbl 1376.68138
[4] S. Hara, T. Hayakawa, H. Sugata, Stability analysis of linear systems with generalized frequency variables and its applications to formation control, in: Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, 2007, pp. 1459-1466.
[5] Hara, S.; Hayakawa, T.; Sugata, H., LTI systems with generalized frequency variables: a unified approach for homogeneous multi-agent dynamical systems, Sice jcmsi, 2, 299-306, (2009)
[6] S. Hara, T. Iwasaki, H. Tanaka, \(H_2\) and \(H_\infty\) norm computations for LTI systems with generalized frequency variables, in: Proceedings of the 2010 American Control Conference, Baltimore, 2010, pp. 1862-1867.
[7] S. Hara, M. Kanno, H. Tanaka, Cooperative gain output feedback stabilization for multi-agent dynamical systems, in: Proceedings of the Joint 48th CDC-28th CCC, Shanghai, China, 2009, pp. 877-882.
[8] H. Tanaka, S. Hara, T. Iwasaki, LMI stability conditions for linear systems with generalized frequency variables, in: Proceedings of the 7th Asian Control Conference, Hong Kong, China, 2009, pp. 136-141.
[9] Kailath, T., Linear systems, (1980), Prentice-Hall Englewood Cliffs, NJ · Zbl 0458.93025
[10] Antsaklis, P.; Michel, A.N., A linear systems primer, (2007), Birkäuser Boston · Zbl 1168.93001
[11] Syrmos, V.L.; Abdallah, C.T.; Dorato, P.; Grigoriadis, K., Static output feedback — a survey, Automatica, 33, 125-137, (1997) · Zbl 0872.93036
[12] Kimura, H., Pole assignment by gain output feedback, IEEE trans. automat. control, 20, 509-516, (1975) · Zbl 0309.93017
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