AUTHORS: Maria Isabel Garcia-Planas
Download as PDF
ABSTRACT: In recent years, due to the relation between cognitive control and mathematical concept of control dynamical systems, there has been growing interest in the descriptive analysis of complex networks with linear dynamics, permeating many aspects from everyday life, obtaining considerable advances in the description of their structural and dynamical properties. Nevertheless, much less effort has been devoted to studying the controllability of the dynamics taking place on them. Concretely, for complex systems is of interest to study the exact controllability, this measure is defined as the minimum set of controls that are needed to steer the whole system toward any desired state. In this paper, a revision of controllability concepts is presented and provides conditions for exact controllability for the multiagent systems
KEYWORDS: Neural network, controllability, exact controllability, eigenvalues, eigenvectors, linear systems
REFERENCES:
[1] J. Assan, A. Lafay, A. Perdon, “Computation of maximal pre-controllability submodules over a Noetherian ring” Systems & Control Letters, vol. 2, no. 3, 1999, pp. 153–161.
[2] F. Cardetti, M. Gordina, A note on local controllability on lie groups. Systems & Control Letters, vol. 57, 2008, pp. 978–979.
[3] C.T. Chen, Introduction to Linear System Theory. Holt, Rinehart and Winston Inc, New York, 1970.
[4] M.I. Garcia-Planas. “Obtaining Consensus of Multi-agent Linear Dynamic Systems”. Advances in Applied and Pure Mathematics, 2005. pp. 1–5.
[5] M.I. Garc´ıa-Planas, “Generalized Controllability Subspcaes for Time-invariant Singular Linear Systems”, Proceedings of Physcon 2011, IPACS Electronic Library, 2011.
[6] M.I. Garc´ıa-Planas, “Exact Controllability of Linear Dynamical Systems: a Geometrical Approach”, Applications of Mathematics. vol. 1, 2017, pp. 37–47, DOI:10.21136/AM.2016.0427-15
[7] M.I. Garcia-Planas, J.L. Dom´ınguez, “Alternative tests for functional and pointwise outputcontrollability of linear time-invariant systems”, Systems & control letters, vol. 62, 2013, no 5, pp. 382–387.
[8] M. I. Garc´ıa-Planas, M.V. Garc´ıa-Camba Vives, M. V. Dyscalculia, mind, calculating brain and education. In EDULEARN18: 10th Annual International Conference on Education and New Learning Technologies: Palma de Mallorca, Spain: July 2-4, 2018: proceedings book, (2018). pp. 0480–0489.
[9] Sh, Gu, F. Pasqualetti, M. Cieslak, Q. K. Telesford, A. B. Yu, A. E. Kahn, J. D. Medaglia, J. M. Vettel, M. B. Miller, S. T. Grafton, D. S. Bassett. “Controllability of structural brain networks”2015. DOI: 10.1038/ncomms9414
[10] M. L. J. Hautus, “Controllability and observability conditions of linear autonomous systems”. Nederl. Akad. Wetensch. Proc. Ser. A 72 = Indag. Math. vol. 31, 1969, pp. 443–448.
[11] A. Heniche, I. Kamwa, “Using measures of controllability and observability for input and output selection”, Proceedings of the 2002 IEEE International Conference on Control Applications, vol. 2, (2002) pp. 1248–1251.
[12] R. E. Kalman, P. L. Falb and M. A. Arbib, “Topics in Mathematical Control Theory”, McGrawHill Book Co., New York-Toronto, Ont.-London 1969.
[13] N. Kriegeskorte Deep Neural Networks: “A New Framework for Modeling Biological Vision and Brain Information Processing”. Annual Review of Vision Science, vol. 1, 2015, pp. 417–46
[14] P. Kundur, Power System Stability and Control, McGraw-Hill, 1994.
[15] D. Leitold, A. Vathy-Fogarassy, J. Abonyi. “Controllability and observability in complex networks - the effect of connection types”. Scientific Reports. 2017;7(151). pmid:28273948
[16] C. Lin, Structural controllability, IEEE Trans. Automat. Contr. vol. 19, 1974, pp. 201–208.
[17] Y. Liu, J. Slotine, A. Barabasi, “Controllabil- ´ ity of complex networks ”, Nature, vol. 473, no (7346), 2011, pp. 167–173.
[18] R. Shields, J. Pearson, “Structural controllability of multi-input linear systems”. IEEE Trans. Automat. Contr, vol. 21, 1976, pp. 203–212.
[19] J. Wang, D. Cheng, X. Hu, “Consensus of multiagent linear dynamics systems, Asian Journal of Control”vol. 10, (2), 2008, pp. 144–155.
[20] D. West Introduction to Graph Theory. Prentice Hall (3rd Edition), 2007.
[21] Z.Z. Yuan, C. Zhao, W.X. Wang, Z.R. Di, Y.C. Lai, “Exact controllability of multiplex networks”, New Journal of Physics, vol. 16, 2014, pp. 1–24.
