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Research Papers

Formation Control Protocols for Nonlinear Dynamical Systems Via Hybrid Stabilization of Sets

[+] Author and Article Information
Wassim M. Haddad

School of Aerospace Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332-0150
e-mail: wm.haddad@aerospace.gatech.edu

Sergey G. Nersesov

Department of Mechanical Engineering,
Villanova University,
Villanova, PA 19085-1681
e-mail: sergey.nersesov@villanova.edu

Qing Hui

Department of Mechanical Engineering,
Texas Tech University,
Lubbock, TX 79409-1021
e-mail: qing.hui@ttu.edu

Masood Ghasemi

Department of Mechanical Engineering,
Villanova University,
Villanova, PA 19085-1681
e-mail: mghase01@villanova.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received April 23, 2013; final manuscript received April 22, 2014; published online July 9, 2014. Assoc. Editor: Shankar Coimbatore Subramanian.

J. Dyn. Sys., Meas., Control 136(5), 051020 (Jul 09, 2014) (13 pages) Paper No: DS-13-1165; doi: 10.1115/1.4027501 History: Received April 23, 2013; Revised April 22, 2014

In this paper, we develop a hybrid control framework for addressing multiagent formation control protocols for general nonlinear dynamical systems using hybrid stabilization of sets. The proposed framework develops a novel class of fixed-order, energy-based hybrid controllers as a means for achieving cooperative control formations, which can include flocking, cyclic pursuit, rendezvous, and consensus control of multiagent systems. These dynamic controllers combine a logical switching architecture with the continuous system dynamics to guarantee that a system generalized energy function whose zero level set characterizes a specified system formation is strictly decreasing across switchings. The proposed approach addresses general nonlinear dynamical systems and is not limited to systems involving single and double integrator dynamics for consensus and formation control or unicycle models for cyclic pursuit. Finally, several numerical examples involving flocking, rendezvous, consensus, and circular formation protocols for standard system formation models are provided to demonstrate the efficacy of the proposed approach.

Copyright © 2014 by ASME
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References

Haddad, W. M., Chellaboina, V., Hui, Q., and Nersesov, S. G., 2007, “Energy- and Entropy-Based Stabilization for Lossless Dynamical Systems Via Hybrid Controllers,” IEEE Trans. Autom. Control, 52(9), pp. 1604–1614. [CrossRef]
Haddad, W. M., Chellaboina, V., and Nersesov, S. G., 2006, Impulsive and Hybrid Dynamical Systems. Stability, Dissipativity, and Control, Princeton University Press, Princeton, NJ.
Mesbahi, M., and Egerstedt, M., 2010, Graph Theoretic Methods in Multiagent Networks, Princeton University Press, Princeton, NJ.
Hui, Q., and Haddad, W. M., 2008, “Distributed Nonlinear Control Algorithms for Network Consensus,” Automatica, 44(9), pp. 2375–2381. [CrossRef]
Chellaboina, V., Haddad, W. M., Hui, Q., and Ramakrishnan, J., 2008, “On System State Equipartitioning and Semistability in Network Dynamical Systems With Arbitrary Time-Delays,” Syst. Control Lett., 57(8), pp. 670–679. [CrossRef]
Hui, Q., Haddad, W. M., and Bhat, S. P., 2008, “Finite-Time Semistability and Consensus for Nonlinear Dynamical Networks,” IEEE Trans. Autom. Control, 53(8), pp. 1887–1900. [CrossRef]
Bhat, S. P., and Bernstein, D. S., 2003, “Nontangency-Based Lyapunov Tests for Convergence and Stability in Systems Having a Continuum of Equilibria,” SIAM J. Control Optim., 42(5), pp. 1745–1775. [CrossRef]
Bhat, S. P., and Bernstein, D. S., 2010, “Arc-Length-Based Lyapunov Tests for Convergence and Stability With Applications to Systems Having a Continuum of Equilibria,” Math. Control Signals Syst., 22(2), pp. 155–184. [CrossRef]
Haddad, W. M., and Chellaboina, V., 2008, Nonlinear Dynamical Systems and Control: A Lyapunov-Based Approach, Princeton University Press, Princeton, NJ.
Haddad, W. M., Chellaboina, V., and Nersesov, S. G., 2005, Thermodynamics: A Dynamical Systems Approach, Princeton University Press, Princeton, NJ.
Strogatz, S. H., 2000, “From Kuramoto to Crawford: Exploring the Onset of Synchronization in Populations of Coupled Oscillators,” Physica D, 143(1–4), pp. 1–20. [CrossRef]
Brown, E., Moehlis, J., and Holmes, P., 2004, “On the Phase Reduction and Response Dynamics of Neural Oscillator Populations,” Neural Comput., 16(4), pp. 673–715. [CrossRef] [PubMed]
Hui, Q., Haddad, W. M., and Bailey, J. M., 2011, “Multistability, Bifurcations, and Biological Neural Networks: A Synaptic Drive Firing Model for Cerebral Cortex Transition in the Induction of General Anesthesia,” Nonlinear Anal. Hybrid Syst., 5(3), pp. 554–573. [CrossRef]
Tanner, H. G., Jadbabaie, A., and Pappas, G. J., 2003, “Stable Flocking of Mobile Agents, Part I: Fixed Topology,” 42nd IEEE Conference on Decision and Control, Maui, HI, December 9–12, pp. 2010–2015. [CrossRef]
Olfati-Saber, R., 2006, “Flocking for Multi-Agent Dynamic Systems: Algorithms and Theory,” IEEE Trans. Autom. Control, 51(3), pp. 401–420. [CrossRef]
Marshall, J. A., Broucke, M. E., and Francis, B. A., 2004, “Formations of Vehicles in Cyclic Pursuit,” IEEE Trans. Autom. Control, 49(11), pp. 1963–1974. [CrossRef]
Lakshmikantham, V., Bainov, D. D., and Simeonov, P. S., 1989, Theory of Impulsive Differential Equations, World Scientific, Singapore.
Bainov, D. D., and Simeonov, P. S., 1989, Systems With Impulse Effect: Stability, Theory and Applications, Ellis Horwood Limited, UK.
Bainov, D. D., and Simeonov, P. S., 1995, Impulsive Differential Equations: Asymptotic Properties of the Solutions, World Scientific, Singapore.
Samoilenko, A. M., and Perestyuk, N. A., 1995, Impulsive Differential Equations, World Scientific, Singapore.
Chellaboina, V., Bhat, S. P., and Haddad, W. M., 2003, “An Invariance Principle for Nonlinear Hybrid and Impulsive Dynamical Systems,” Nonlinear Anal. Theory Methods Appl., 53(3–4), pp. 527–550. [CrossRef]
Michel, A. N., Wang, K., and Hu, B., 2001, Qualitative Theory of Dynamical Systems: The Role of Stability Preserving Mappings, Marcel Dekker, Inc., New York.
Grizzle, J. W., Abba, G., and Plestan, F., 2001, “Asymptotically Stable Walking for Biped Robots: Analysis Via Systems With Impulse Effects,” IEEE Trans. Autom. Control, 46(1), pp. 51–64. [CrossRef]
Guillemin, V., and Pollack, A., 1974, Differential Topology, Prentice-Hall, Englewood Cliffs, NJ.
Dubrovin, B. A., Fomenko, A. T., and Novikov, S. P., 1985, Modern Geometry—Methods and Applications: Part II: The Geometry and Topology of Manifolds, Springer, New York.
Goebel, R., and Teel, A. R., 2006, “Solutions to Hybrid Inclusions Via Set and Graphical Convergence With Stability Theory Applications,” Automatica, 42(4), pp. 573–587. [CrossRef]
Bernstein, D. S., 2005, Matrix Mathematics, Princeton University Press, Princeton, NJ.
Justh, E. W., and Krishnaprasad, P. S., 2004, “Equilibria and Steering Laws for Planar Formations,” Syst. Control Lett., 52(1), pp. 25–38. [CrossRef]
Hui, Q., and Haddad, W. M., 2007, “Continuous and Hybrid Distributed Control for Multiagent Coordination: Consensus, Flocking, and Cyclic Pursuit,” American Control Conference (ACC '07), New York, July 9–13, pp. 2576–2581. [CrossRef]
El-Hawwary, M. I., and Maggiore, M., 2013, “Distributed Circular Formation Stabilization for Dynamic Unicycles,” IEEE Trans. Autom. Control, 58(1), pp. 149–162. [CrossRef]
Kasdin, N. J., and Paley, D. A., 2011, Engineering Dynamics, Princeton University Press, Princeton, NJ.

Figures

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Fig. 1

Agent positions in the plane

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Fig. 2

Control forces in x direction

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Fig. 3

Control forces in y direction

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Fig. 4

Velocities in x direction

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Fig. 5

Velocities in y direction

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Fig. 6

Generalized energy functions Vp(xp(t)) and Vc(xc(t), xp(t)) versus time

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Fig. 7

Agent positions in the plane

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Fig. 8

Control forces in x direction

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Fig. 9

Control forces in y direction

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Fig. 10

Generalized energy functions Vp(xp(t)) and Vc(xc(t), xp(t)) versus time

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Fig. 11

Plant states xp versus time

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Fig. 12

Control inputs versus time

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Fig. 13

Generalized energy functions Vp and Vc versus time

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Fig. 14

Agent positions in the plane

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Fig. 15

Agent velocities versus time

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Fig. 16

Agent angular velocities versus time

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Fig. 17

Agent orientations versus time

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