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Stabilization of sets with application to multi-vehicle coordinated motion

Title:

Stabilization of sets with application to multi-vehicle coordinated motion

Nersesov, Sergey G., Ghorbanian, Parham and Aghdam, Amir G. (2010) Stabilization of sets with application to multi-vehicle coordinated motion. Automatica, 46 (9). pp. 1419-1427. ISSN 00051098

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Official URL: http://dx.doi.org/10.1016/j.automatica.2010.06.009

Abstract

In this paper, we develop stability and control design framework for time-varying and time-invariant sets of nonlinear dynamical systems using vector Lyapunov functions. Several Lyapunov functions arise naturally in multi-agent systems, where each agent can be associated with a generalized energy function which further becomes a component of a vector Lyapunov function. We apply the developed control framework to the problem of multi-vehicle coordinated motion to design distributed controllers for individual vehicles moving in a specified formation. The main idea of our approach is that a moving formation of vehicles can be characterized by a time-varying set in the state space, and hence, the problem of distributed control design for multi-vehicle coordinated motion is equivalent to the design of stabilizing controllers for time-varying sets of nonlinear dynamical systems. The control framework is shown to ensure global exponential stabilization of multi-vehicle formations. Finally, we implement the feedback stabilizing controllers for time-invariant sets to achieve global exponential stabilization of static formations of multiple vehicles.

Divisions:Concordia University > Gina Cody School of Engineering and Computer Science > Electrical and Computer Engineering
Item Type:Article
Refereed:Yes
Authors:Nersesov, Sergey G. and Ghorbanian, Parham and Aghdam, Amir G.
Journal or Publication:Automatica
Date:2010
Digital Object Identifier (DOI):10.1016/j.automatica.2010.06.009
Keywords:Stabilization of sets; Vector Lyapunov functions; Multi-vehicle systems; Coordinated motion; Cooperative control
ID Code:975172
Deposited By: DANIELLE DENNIE
Deposited On:22 Jan 2013 14:21
Last Modified:18 Jan 2018 17:39

References:

Bellman, 1962 R. Bellman Vector Lyapunov functions SIAM Journal on Control, 1 (1962), pp. 32–34

Bernstein, 2005 D.S. Bernstein Matrix mathematics Princeton University Press, Princeton, NJ (2005)

Bullo et al., 2009 F. Bullo, J. Cortéz, S. Martinéz Distributed control of robotic networks Princeton University Press, Princeton, NJ (2009)

Chandler et al., 2001 Chandler, P. R., Pachter, M., & Rasmussen, S. (2001). UAV cooperative control. In Proc. Amer. contr. conf. Arlington, VA (pp. 50–55).

Corfmat and Morse, 1976 J. Corfmat, A. Morse Decentralized control of linear multivariable systems Automatica, 12 (1976), pp. 476–495

Desai et al., 2001 J.P. Desai, J.P. Ostrowski, V. Kumar Modeling and control of formations of nonholonomic mobile robots IEEE Transactions on Robotics and Automation, 17 (2001), pp. 905–908

Diestel, 1997 R. Diestel Graph theory Springer-Verlag, New York, NY (1997)

Egerstedt et al., 2001 M. Egerstedt, X. Hu, A. Stotsky Control of mobile platforms using a virtual vehicle approach IEEE Transactions on Automatic Control, 46 (2001), pp. 1777–1782

Fax and Murray, 2004 J.A. Fax, R.M. Murray Information flow and cooperative control of vehicle formations IEEE Transactions on Automatic Control, 49 (2004), pp. 1465–1476

Haddad et al., 2010 W.M. Haddad, V. Chellaboina, Q. Hui Nonnegative and compartmental dynamical systems Princeton University Press, Princeton, NJ (2010)

Hui and Haddad, 2008 Q. Hui, W.M. Haddad Distributed nonlinear control algorithms for network consensus Automatica, 44 (2008), pp. 2375–2381

Isidori, 1995 A. Isidori Nonlinear control systems Springer-Verlag, Berlin (1995)

Jadbabaie et al., 2003 A. Jadbabaie, J. Lin, A.S. Morse Coordination of groups of mobile autonomous agents using nearest neighbor rules IEEE Transactions on Automatic Control, 48 (2003), pp. 988–1001

Khalil, 2002 H.K. Khalil Nonlinear systems (3rd ed.)Prentice-Hall, Upper Saddle River, NJ (2002)

Lakshmikantham et al., 1991 V. Lakshmikantham, V.M. Matrosov, S. Sivasundaram Vector Lyapunov functions and stability analysis of nonlinear systems Kluwer Academic Publishers, Dordrecht, Netherlands (1991)

Lakshmikantham and Sivasundaram, 1998 V. Lakshmikantham, S. Sivasundaram Stability of moving invariant sets and uncertain dynamic systems on time scales Computers and Mathematics with Applications, 36 (1998), pp. 339–346

Leela and Shahzad, 1996 S. Leela, N. Shahzad On stability of moving conditionally invariant sets Nonlinear Analysis: Theory, Methods and Applications, 27 (7) (1996), pp. 797–800

Leonard and Fiorelli, 2001 Leonard, N. E., & Fiorelli, E. (2001). Virtual leaders, artificial potentials, and coordinated control of groups. In Proc. IEEE conf. dec. contr. Orlando, FL(pp. 2968–2873).

Marshall et al., 2004 J.A. Marshall, M.E. Broucke, B.A. Francis Formations of vehicles in cyclic pursuit IEEE Transactions on Automatic Control, 49 (2004), pp. 1963–1974


Martynyuk-Chernienko, 1999 Yu.A. Martynyuk-Chernienko On the stability of motion of uncertain systems International Applied Mechanics, 35 (2) (1999), pp. 212–216

Matrosov, 1972 V.M. Matrosov Method of vector Lyapunov functions of interconnected systems with distributed parameters (survey) Avtomatika i Telemekhanika, 33 (1972), pp. 63–75 (in Russian)

Mesbahi, 2005 M. Mesbahi On state-dependent dynamic graphs and their controllability properties IEEE Transactions on Automatic Control, 50 (2005), pp. 387–392

Murray, 2007 R.M. Murray Recent research in cooperative control of multi-vehicle systems Journal of Dynamic Systems, Measurement and Control, 129 (2007), pp. 571–583

Nersesov and Haddad, 2006 S.G. Nersesov, W.M. Haddad On the stability and control of nonlinear dynamical systems via vector Lyapunov functions IEEE Transactions on Automatic Control, 51 (2) (2006), pp. 203–215


Olfati-Saber, 2006 R. Olfati-Saber Flocking for multi-agent dynamic systems: algorithms and theory IEEE Transactions on Automatic Control, 51 (2006), pp. 401–420

Olfati-Saber and Murray, 2002 Olfati-Saber, R., & Murray, R. M. (2002). Distributed cooperative control of multiple vehicle formations using structural potential functions. In IFAC world congr. Barcelona, Spain.

Örgen et al., 2002 P. Örgen, M. Egerstedt, X. Hu A control Lyapunov function approach to multiagent coordination IEEE Transactions on Robotics and Automation, 18 (5) (2002), pp. 847–851

Ren and Beard, 2008 W. Ren, R.W. Beard Distributed consensus in multi-vehicle cooperative control Springer-Verlag, London, UK (2008)

Šiljak, 1978 D.D. Šiljak Large-scale dynamic systems: stability and structure Elsevier, North-Holland Inc., New York, NY (1978)

Smith et al., 2001 Smith, T.R., Hanssmann, H., & Leonard, N.E. (2001). Orientation control of multiple underwater vehicles with symmetry-breaking potentials. In Proc. IEEE conf. dec. contr. Orlando, FL (pp. 4598–4603).

Sontag, 1989 E.D. Sontag A universal construction of Artstein’s theorem on nonlinear stabilization Systems & Control Letters, 13 (1989), pp. 117–123

Tanner et al., 2007 H.G. Tanner, A. Jadbabaie, G.J. Pappas
Flocking in fixed and switching networks IEEE Transactions on Automatic Control, 52 (2007), pp. 863–868
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