Abstract
This chapter considers synchronization problems for homogeneous linear continuous-time multi-agent systems (MAS). A multi-agent system is homogeneous when the dynamics of all agents are identical. For homogeneous systems, we will primarily consider state synchronization where the differences between the states of different agents converge to zero. We also address the case of formation where the differences between states of different agents converge to, a priori given, vectors.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Arcak, M.: Passivity as a design tool for group coordination. IEEE Trans. Autom. Control 52(8), 1380–1390 (2007)
Bai, H., Arcak, M., Wen, J.: Cooperative Control Design: A Systematic, Passivity-Based Approach. Communications and Control Engineering. Springer, Berlin (2011)
Blondel, V., Gevers, M.: Simultaneous stabilizability of three linear systems is rationally undecidable. Math. Control Signals Syst. 6(2), 135–145 (1993)
Boyd, S.P., Doyle, J.C.: Comparison of peak and RMS gains for discrete-time systems. Syst. Control Lett. 9(1), 1–6 (1987)
Chopra, N., Spong, W.: Output synchronization of nonlinear systems with relative degree one. In: Blondel, V.D., Boyd, S.P., Kimura, H. (eds.). Recent Advances in Learning And Control. Lecture Notes in Control and Information Sciences, vol. 371, pp. 51–64. Springer, London (2008)
Chopra, N., Spong, W.: Passivity-based control of multi-agent systems. In: Kawamura, S., Svinin, M. (eds.). Advances in Robot Control: From Everyday Physics to Human-Like Movements, pp. 107–134. Springer, Heidelberg (2008)
Doyle, J.C., Glover, K., Khargonekar, P.P., Francis, B.A.: State space solutions to standard H 2 and H ∞ control problems. IEEE Trans. Autom. Control 34(8), 831–847 (1989)
Gantmacher, F.R.: The Theory of Matrices. Chelsea, New York (1959)
Grip, H.F., Saberi, A., Stoorvogel, A.A.: Synchronization in networks of minimum-phase, non-introspective agents without exchange of controller states: homogeneous, heterogeneous, and nonlinear. Automatica 54, 246–255 (2015)
Hatanaka, T., Chopra, N., Fujita, M., Spong, M.W.: Passivity-Based Control and Estimation in Networked Robotics. Springer, Heidelberg (2015)
Lafferriere, G., Williams, A., Caughman, J., Veerman, J.J.P.: Decentralized control of vehicle formations. Syst. Control Lett. 54(9), 899–910 (2005)
Li, Z., Duan, Z., Chen, G., Huang, L.: Consensus of multi-agent systems and synchronization of complex networks: a unified viewpoint. IEEE Trans. Circ. Syst.-I Regul. Pap. 57(1), 213–224 (2010)
Lin, Z.: Low Gain Feedback. Lecture Notes in Control and Information Sciences. Springer, Berlin (1998)
Lin, Z., Saberi, A.: Low-and-high gain design technique for linear systems subject to input saturation – a direct method. Int. J. Robust Nonlinear Control 7(12), 1071–1101 (1997)
Liu, Z., Zhang, M., Saberi, A., Stoorvogel, A.A.: State synchronization of multi-agent systems via static or adaptive nonlinear dynamic protocols. Automatica 95, 316–327 (2018)
Ma, C.Q., Zhang, J.F.: Necessary and sufficient conditions for consensusability of linear multi-agent systems. IEEE Trans. Autom. Control 55(5), 1263–1268 (2010)
Olfati-Saber, R., Murray, R.M.: Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control 49(9), 1520–1533 (2004)
Ren, W., Atkins, E.: Distributed multi-vehicle coordinate control via local information. Int. J. Robust Nonlinear Control 17(10–11), 1002–1033 (2007)
Saberi, A., Sannuti, P.: Time-scale structure assignment in linear multivariable systems using high-gain feedback. Int. J. Control 49(6), 2191–2213 (1989)
Saberi, A., Chen, B.M., Sannuti, P.: Loop Transfer Recovery: Analysis and Design. Springer, Berlin (1993)
Saberi, A., Stoorvogel, A.A., Sannuti, P.: Internal and External Stabilization of Linear Systems with Constraints. Birkhäuser, Boston (2012)
Scardovi, L., Sepulchre, R.: Synchronization in networks of identical linear systems. Automatica 45(11), 2557–2562 (2009)
Schumacher, J.M.: The role of the dissipation matrix in singular optimal control. Syst. Contr. Lett. 2(5), 262–266 (1983)
Seo, J.H., Shim, H., Back, J.: Consensus of high-order linear systems using dynamic output feedback compensator: low gain approach. Automatica 45(11), 2659–2664 (2009)
Stoorvogel, A.A.: The H ∞ Control Problem: A State Space Approach. Prentice-Hall, Englewood Cliffs (1992)
Stoorvogel, A.A.: The H ∞ control problem with zeros on the boundary of the stability domain. Int. J. Control 63(6), 1029–1053 (1996)
Stoorvogel, A.A., Zhang, M., Saberi, A., Grip, H.F.: Synchronization in networks of weakly-non-minimum-phase, non-introspective agents without exchange of controller states. In: American Control Conference, Portland, pp. 3548–3552 (2014)
Stoorvogel, A.A., Saberi, A., Zhang, M.: Synchronization for heterogeneous networks of weakly-non-minimum-phase, non-introspective agents without exchange of controller states. In: American Control Conference, Boston, pp. 5187–5192 (2016)
Stoorvogel, A.A., Saberi, A., Zhang, M.: Solvability conditions and design for state synchronization of multi-agent systems. Automatica 84, 43–47 (2017)
Tuna, S.E.: LQR-based coupling gain for synchronization of linear systems. ar**v:0801.3390v1 (2008)
Tuna, S.E.: Conditions for synchronizability in arrays of coupled linear systems. IEEE Trans. Autom. Control 55(10), 2416–2420 (2009)
Wang, J., Cheng, D., Hu, X.: Consensus of multi-agent linear dynamic systems. Asian J. Control 10(2), 144–155 (2008)
Wieland, P., Kim, J.S., Scheu, H., Allgöwer, F.: On consensus in multi-agent systems with linear high-order agents. In: Proceedings of the 17th IFAC World Congress, Seoul, pp. 1541–1546 (2008)
Willems, J.C.: Least squares stationary optimal control and the algebraic Riccati equation. IEEE Trans. Autom. Control 16(6), 621–634 (1971)
Wonham, W.M.: Linear Multivariable Control: A Geometric Approach, 3rd edn. Springer, New York (1985)
Wu, C.W.: Synchronization in Complex Networks of Nonlinear Dynamical Systems. World Scientific, Singapore (2007)
Wu, C.W., Chua, L.O.: Application of graph theory to the synchronization in an array of coupled nonlinear oscillators. IEEE Trans. Circ. Syst.-I Fundam. Theory Appl. 42(8), 494–497 (1995)
Wu, C.W., Chua, L.O.: Application of Kronecker products to the analysis of systems with uniform linear coupling. IEEE Trans. Circ. Syst.-I Fundam. Theory Appl. 42(10), 775–778 (1995)
**a, T., Scardovi, L.: Output-feedback synchronizability of linear time-invariant systems. Syst. Control Lett. 94, 152–158 (2016)
**a, T., Scardovi, L.: Synchronization of linear time-invariant systems on rooted graphs. In: Proceedings 55th Conference on Decision and Control (CDC), Las Vegas, pp. 4376–4381 (2016)
Yang, T., Roy, S., Wan, Y., Saberi, A.: Constructing consensus controllers for networks with identical general linear agents. Int. J. Robust Nonlinear Control 21(11), 1237–1256 (2011)
Yang, T., Saberi, A., Stoorvogel, A.A., Grip, H.F.: Output synchronization for heterogeneous networks of introspective right-invertible agents. Int. J. Robust Nonlinear Control 24(13), 1821–1844 (2014)
Yao, J., Guan, Z.-H., Hill, D.J.: Passivity-based control and synchronization of general complex dynamical networks. Automatica 45(9), 2107–2113 (2009)
Zhang, M., Saberi, A., Grip, H.F., Stoorvogel, A.A.: “\(\mathcal {H}_{\infty }\) almost output synchronization for heterogeneous networks without exchange of controller states. IEEE Trans. Control Netw. Syst. 2(4), 348–357 (2015)
Zhao, J., Hill, D.J., Liu, T.: Passivity-based output synchronization of dynamical network with non-identical nodes. In: Proceedings of 49th Conference on Decision and Control (CDC), Atlanta, pp. 7351–7356 (2010)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2022 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Saberi, A., Stoorvogel, A.A., Zhang, M., Sannuti, P. (2022). Synchronization of Continuous-Time Linear MAS. In: Synchronization of Multi-Agent Systems in the Presence of Disturbances and Delays. Systems & Control: Foundations & Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-88148-1_2
Download citation
DOI: https://doi.org/10.1007/978-3-030-88148-1_2
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-88147-4
Online ISBN: 978-3-030-88148-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)