Achieving coordination tasks in finite time via nonsmooth gradient flows

Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05

Volumn 2005, Issue , 2005, Pages 6376-6381

  Cortés, Jorge ^a  

^a Santa Cruz   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ASYMPTOTIC STABILITY; CONVERGENCE OF NUMERICAL METHODS; FINITE AUTOMATA;

COORDINATION TASKS; DIFFERENTIABLE FUNCTION; FINITE TIME; NETWORK CONSENSUS PROBLEMS;

GRADIENT METHODS;

EID: 33847205325     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2005.1583184     Document Type: Conference Paper

References (23)

1. W. M. Hirsch and S. Smale, Differential Equations, Dynamical Systems and Linear Algebra. New York, NY: Academic Press, 1974.
2. U. Helmke and J. Moore, Optimization and Dynamical Systems. New York: Springer Verlag, 1994.
3. D. P. Bertsekas and J. N. Tsitsiklis, Parallel and Distributed Computation: Numerical Methods. Belmont, MA: Athena Scientifi c, 1997.
4. F. H. Clarke, Optimization and Nonsmooth Analysis. Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley & Sons, 1983.
5. A. Bacciotti and F. Ceragioli, "Stability and stabilization of discontinuous systems and nonsmooth Lyapunov functions," ESAIM. Control, Optimisation & Calculus of Variations, vol. 4, pp. 361-376, 1999.
6. A. F. Filippov, Differential Equations with Discontinuous Righthand Sides, vol. 18 of Mathematics and Its Applications. Dordrecht, The Netherlands: Kluwer Academic Publishers, 1988.
7. D. Shevitz and B. Paden, "Lyapunov stability theory of nonsmooth systems," IEEE Transactions on Automatic Control, vol. 39, no. 9, pp. 1910-1914, 1994.
8. E. P. Ryan, "Finite-time stabilization of uncertain nonlinear planar systems," Dynam. Control, vol. 1, pp. 83-94, 1991.
9. S. P. Bhat and D. S. Bernstein, "Finite-time stability of continuous autonomous systems," SIAM Journal on Control and Optimization, vol. 38, no. 3, pp. 751-766, 2000.
10. J. M. Coron, "On the stabilization in fi nite time of locally controllable systems by means of continuous time-varying feedback laws," SIAM Journal on Control and Optimization, vol. 33, pp. 804-833, 1995.
11. V. Gazi and K. M. Passino, "Stability analysis of swarms," IEEE Transactions on Automatic Control, vol. 48, no. 4, pp. 692-697, 2003.
12. P. Ögren, E. Fiorelli, and N. E. Leonard, "Cooperative control of mobile sensor networks: adaptive gradient climbing in a distributed environment," IEEE Transactions on Automatic Control, vol. 49, no. 8, pp. 1292-1302, 2004.
13. H. Tanner, A. Jadbabaie, and G. J. Pappas, "Flocking in fixed and switching networks," IEEE Transactions on Automatic Control, 2005. Submitted.
14. R. Olfati-Saber and R. M. Murray, "Consensus problems in networks of agents with switching topology and time-delays," IEEE Transactions on Automatic Control, vol. 49, no. 9, pp. 1520-1533, 2004.
15. J. Cortés and F. Bullo, "Coordination and geometric optimization via distributed dynamical systems," SIAM Journal on Control and Optimization, 2005. To appear.
16. J. Cortés, S. Martínez, and F. Bullo, "Spatially- distributed coverage optimization and control with limited-range interactions," ESAIM. Control, Optimisation & Calculus of Variations, 2005. To appear.
17. J. Cortés, "Finite-time convergent gradient fbws with applications to motion coordination," Systems & Control Letters, Sept. 2005. Submitted.
18. R. Diestel, Graph Theory, vol. 173 of Graduate Texts in Mathematics. New York: Springer Verlag, second ed., 2000.
19. M. de Berg, M. van Kreveld, and M. Overmars, Computational Geometry: Algorithms and Applications. New York: Springer Verlag, 1997.
20. J. W. Jaromczyk and G. T. Toussaint, "Relative neighborhood graphs and their relatives," Proceedings of the IEEE, vol. 80, no. 9, pp. 1502-1517, 1992.
21. H. Ando, Y. Oasa, I. Suzuki, and M. Yamashita, "Distributed memoryless point convergence algorithm for mobile robots with limited visibility," IEEE Transactions on Robotics and Automation, vol. 15, no. 5, pp. 818-828, 1999.
22. D. P. Spanos, R. Olfati-Saber, and R. M. Murray, "Distributed sensor fusion using dynamic consensus," in IFAC World Congress, (Prague, CZ), July 2005. Electronic proceedings.
23. L. Xiao, S. Boyd, and S. Lall, "A scheme for asynchronous distributed sensor fusion based on average consensus," in Fourth International Conference on Information Processing in Sensor Networks (IPSN'05), (Los Angeles, CA), 2005. To appear.