Controllability of Linear Time Invariant Networked Systems: A Review

Authors

  • Abhijith Ajayakumar Department of Mathematics, Indian Institute of Space Science and Technology, Thiruvananthapuram 695 547
  • Raju K. George Department of Mathematics, Indian Institute of Space Science and Technology, Thiruvananthapuram 695 547

Keywords:

Controllability, LTI systems, Networked Control Systems, Network Topology

Abstract

Controllability of networked linear time invariant (LTI) systems has been gaining much attention in the academia, in the last decade. In this paper, we review some of the basic concepts, notable results and recent developments in the studies of networked systems. Different results of controllability of LTI systems based on network topology, node dynamics, external control inputs and inner coupling of the dynamical systems are analysed here and a future research perspective is highlighted.

Downloads

Download data is not yet available.

Downloads

Published

2024-05-08

How to Cite

Ajayakumar , A., & George, R. K. (2024). Controllability of Linear Time Invariant Networked Systems: A Review. Chetana: An Ivanian Journal for Scientific Research, 1(1), 26–44. Retrieved from https://marivanioscollegejournals.com/index.php/chetana/article/view/43

Issue

Section

Articles

References

Abhijith Ajayakumar and Raju K George. Controllability of lti networked systems with heterogeneous dynamics. arXiv preprint arXiv:2012.10665, 2020.

Abhijith Ajayakumar and Raju K George. A note on controllability of directed networked system with heterogeneous dynamics. IEEE Transactions on Control of NetworkSystems, 2022.

Danielle S Bassett and Olaf Sporns. Network neuroscience. Nature neuroscience, 20(3): 353–364, 2017.

Lachlan Blackhall and David J Hill. On the structural controllability of networks of linear systems. IFACProceedingsVolumes, 43(19):245–250,2010.

Airlie Chapman and Mehran Mesbahi. On strong structural controllability of networked systems: A constrained matching approach. In 2013 American Control Conference, pages 6126–6131. IEEE, 2013

Christian Commault. Structural controllability of networks with dynamical structured nodes. IEEE Transactions on Automatic Control, 65(6):2736–2742, 2019.

Christian Commault and Alain Kinangou. Generic controllability of networks with identical siso dynamical nodes. IEEE Transactions on Control of Network Systems, 7(2):855–865, 2019.

Hassan Farhangi. The path of the smart grid. IEEE power and energy magazine, 8(1):18–28, 2009.

Shi Gu, Fabio Pasqualetti, Matthew Cieslak, Qawi K Telesford, B Yu Alfred, Ari E Kahn, John D Medaglia, Jean M Vettel, Michael B Miller, Scott T Grafton, et al. Controllability of structural brain networks. Nature communications, 6(1):1–10, 2015.

of structural brain networks. Nature communications, 6(1):1–10, 2015.

Reze Haghighi and Chien Chern Cheah. Topology-based controllability problem in network systems. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 47(11): 3077–3088, 2016.

Yuqing Hao, Zhisheng Duan, and Guanrong Chen. Further on the controllability of networked mimo lti systems. International Journal of Robust and Nonlinear Control, networked mimo lti systems. International Journal of Robust and Nonlinear Control, 28(5):1778–1788, 2018.

Roger A Horn and Charles R Johnson. Topics in matrix analysis. Cambridge university press, 1994.

press, 1994.

Mohan C Joshi and Raju K George. Controllability of nonlinear systems. Numerical Functional Analysis and Optimization, 10(1-2):139–166, 1989.

Rudolf E Kalman. On the general theory of control systems. In Proceedings First International Conference on Automatic Control, Moscow, USSR, pages 481–492, 1960.

Rudolf E Kalman. Canonical structure of linear dynamical systems. Proceedings of the National Academy of Sciences of the United States of America, 48(4):596, 1962.

Zhi Kong, Lianqian Cao, Lifu Wang, and Ge Guo. Controllability of heterogeneous networked systems with nonidentical inner-coupling matrices. IEEE Transactions on Control of Network Systems, 2021.

Ching-Tai Lin. Structural controllability. IEEE Transactions on Automatic Control, 19(3): 201–208, 1974.

Xiaomeng Liu, Hai Lin, and Ben M Chen. Graph-theoretic characterisations of structural controllability for multi-agent system with switching topology. International Journal of Control, 86(2):222–231, 2013.

Shima Sadat Mousavi and Mohammad Haeri. Controllability analysis of networks through their topologies. In 2016 IEEE 55th Conference on Decision and Control (CDC), pages 4346–4351. IEEE, 2016.

Jianbin Mu, Jing Wu, Ning Li, Xiaohu Zhang, and Shaoyuan Li. Structural controllability of networked systems with general heterogeneous subsystems. Asian Journal of Control, 24(3):1321–1332, 2022.

V Muni and Raju K George. Controllability of networked higher-dimensional systems with one-dimensional communications having multiple constant time-delays in control. International Conference on Advances in Pure and Applied Mathematics, 2018.

Herbert G Tanner. On the controllability of nearest neighbor interconnections. In 2004 43rd IEEE Conference on Decision and Control (CDC)(IEEE Cat. No. 04CH37601), volume 3, pages 2467–2472. IEEE, 2004

William J Terrell. Stability and stabilization: an introduction. Princeton University Press, 2009.

Le-Zhi Wang, Ri-Qi Su, Zi-Gang Huang, Xiao Wang, Wen-Xu Wang, Celso Grebogi, and Ying-Cheng Lai. A geometrical approach to control and controllability of nonlinear dynamical networks. Nature communications, 7(1):1–11, 2016a.

Lin Wang, Guanrong Chen, Xiaofan Wang, and Wallace KS Tang. Controllability of networked mimo systems. Automatica, 69:405–409, 2016b.

Lin Wang, Xiaofan Wang, and Guanrong Chen. Controllability of networked higher-dimensional systems with one-dimensional communication. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 375(2088):20160215, 2017a.

Peiru Wang, Linying Xiang, and Fei Chen. Controllability of heterogeneous networked mimo systems. In 2017 International Workshop on Complex Systems and Networks (IWCSN), pages 45– 49. IEEE, 2017b.

Andrew J Whalen, Sean N Brennan, Timothy D Sauer, and Steven J Schiff. Observability and controllability of nonlinear networks: The role of symmetry. Physical Review X, 5(1): 011005, 2015

Stefan Wuchty. Controllability in protein interaction networks. Proceedings of the National Academy of Sciences, 111(19):7156–7160, 2014.

Linying Xiang, Fei Chen, Wei Ren, and Guanrong Chen. Advances in network controllability. IEEE Circuits and Systems Magazine, 19(2):8–32, 2019a.

Linying Xiang, Peiru Wang, Fei Chen, and Guanrong Chen. Controllability of directed networked mimo systems with heterogeneous dynamics. IEEE Transactions on Control of Network Systems, 2019b.

AY Yazıcıo ̆glu, Waseem Abbas, and Magnus Egerstedt. Graph distances and controllability of networks. IEEE Transactions on Automatic Control, 61(12):4125–4130, 2016.

Jorge Gomez,Tejeda Zan ̃udo, Gang Yang, and R ́eka Albert. Structure-based control of complex networks with nonlinear dynamics. Proceedings of the National Academy of Sciences, 114(28):7234–7239, 2017.

Yong Zhang, Gong-You Tang, and Nai-Ping Hu. Non-fragile control for nonlinear networked control systems with long time-delay. Computers & Mathematics with Applications, 57 (10):1630–1637, 2009

F. H. Zhu and Z. Q. Chen. Advanced Analysis and Analytic Geometry. Science Press. Beijing, China, 2018.