Abstract
In natural flocks/swarms, it is very appealing that low-level individual intelligence and communication can yield advanced coordinated collective behaviors such as congregation, synchronization and migration. Firstly, we seek to understand the role of predictive mechanisms in the forming and evolving of flocks/swarms by using both numerical simulations and mathematical analyses. Secondly, by incorporating some predictive mechanism into a few pinning nodes, we show that convergence procedure to consensus can be substantially accelerated in networks of interconnected dynamic agents while physically maintaining the network topology. Such an acceleration stems from the compression mechanism of the eigenspectrum of the state matrix conferred by the predictive mechanism. Thirdly, some model predictive control protocols are developed to achieve consensus for a class of discrete-time double-integrator multi-agent systems with input constraints. Associated sufficient conditions such as that the proximity net has a directed spanning tree and that the sampling period is sufficiently small are proposed. Moreover, the control horizon is extended to larger than one, which endows sufficient degrees of freedom to accelerate the convergence to consensus.
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Notes
- 1.
\(\mathscr {N}(i)\) denotes the set of neighbors of i. More precisely, we say that a node j is a neighbor of a node i, denoted by \(j\in \mathscr {N}(i)\) if, and only if, the corresponding element of the associated adjacency matrix \(a_{ij}\ne 0\).
References
Cao, Y., Ren, W.: LQR-based optimal linear Consensus algorithms. In: Proceedings of American Control Conference, pp. 5204–5209 (2009)
Cao, Y., Ren, W.: Sampled-data discrete-time coordination algorithms for double-integrator dynamics under dynamic directed interaction. Int. J. Control 83, 506–515 (2010)
Cheng, Z., Zhang, H.T., Fan, M., Chen, G.: Distributed consensus of multi-agent systems with input constraints: a model predictive control approach. IEEE Trans. Circuits Syst. I 62, 825–834 (2014)
Conway, J.H., Guy, R.K.: The Book of Numbers. Springer, New York (1996)
Couzin, I.D., Krause, J., Franks, N.R., Levin, S.A.: Effective leadership and decision-making in animal groups on the move. Nature 433, 513–516 (2005)
Gazi, V., Passino, K.M.: Stability analysis of swarms. IEEE Trans. Autom. Control 48, 692–697 (2003)
Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge University Press, Cambridge (1990)
Li, X., Wang, X., Chen, G.: Pinning a complex dynamical network to its equilibrium. IEEE Trans. Circuits. Syst. I 51, 297–2087 (2004)
Ljung, L.: System Identification: Theory for the User. Prentice-Hall Inc., Englewood Cliffs (1999)
Maciejowski, J.M.: Predictive Control with Constraints. Cambridge University Press, Cambridge (2002)
Mayne, D.Q., Rawlings, J.B., Rao, C.V., Scokaer, P.O.M.: Constrained model predictive control: stability and optimality. Automatica 36, 789–814 (2000)
Olfati-Saber, R., Murray, R.: Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control 49, 1520–1533 (2004)
Qin, J., Gao, H.: A sufficient condition for convergence of sampled-data consensus for double-integrator dynamics with nonuniform and time-varying communication delays. IEEE Trans. Autom. Control 57, 2417–2422 (2012)
Qin, S.J., Badgwell, T.A.: A survey of industrial model predictive control technology. Control Eng. Pract. 11, 733–764 (2003)
Ren, W., Beard, R.W.: Consensus seeking in multiagents systems under dynamically changing interaction topologies. IEEE Trans. Autom. Control 50, 655–661 (2005)
Ren, W., Beard, R.W., Arkins, E.M.: Information consensus in multivehicle cooperative control. IEEE Control Syst. Mag. 71, 71–82 (2007)
Vicsek, T., Czirók, A., Ben-Jacob, E., Cohen, I., Shochet, O.: Novel type of phase transition in a system of self-driven particles. Phys. Rev. Lett. 75, 1226–1229 (1995)
Wang, X.F., Li, X., Lu, J.: Control and flocking of networked systems via pinning. IEEE Circuit Syst. Mag. 10, 83–91 (2010)
Watts, D.J., Strogatz, S.H.: Collective dynamics of small-world networks. Nature 393, 440–443 (1998)
**ao, L., Boyd, S.: Fast linear iterations for distributed averaging. Syst. Control Lett. 53, 65–78 (2004)
Acknowledgments
This work was supported by the National Natural Science Foundation of China (NNSFC) under Grants 61322304, 51328501and 51120155001, the Natural Science Foundation of Hubei Province under Grant 2012FFA009 and the Research Fund for the Doctoral Program of Higher Education of China under Grant 20130142110050.
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Zhang, HT., Cheng, Z., Fan, MC., Wu, Y. (2016). Collective Behavior Coordination with Predictive Mechanisms. In: Lü, J., Yu, X., Chen, G., Yu, W. (eds) Complex Systems and Networks. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47824-0_11
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DOI: https://doi.org/10.1007/978-3-662-47824-0_11
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