Finite-time convergent gradient flows with applications to network consensus

Automatica

Volumn 42, Issue 11, 2006, Pages 1993-2000

  Cortés, Jorge ^a  

^a Santa Cruz   (United States)

Author keywords

Finite time convergence; Gradient flows; Multi agent systems; Network consensus; Nonsmooth analysis

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FUNCTION EVALUATION; MULTI AGENT SYSTEMS; STABILITY;

FINITE-TIME CONVERGENCE; GRADIENT FLOWS; NETWORK CONSENSUS; NONSMOOTH ANALYSIS;

GRADIENT METHODS;

EID: 33748930431     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2006.06.015     Document Type: Article

References (20)

1. Bacciotti A., and Ceragioli F. Stability and stabilization of discontinuous systems and nonsmooth Lyapunov functions. ESAIM. Control, Optimisation & Calculus of Variations 4 (1999) 361-376
2. Bertsekas D.P., and Tsitsiklis J.N. Parallel and distributed computation: Numerical methods (1997), Athena Scientific, Belmont, MA ISBN 1886529019
3. Bhat S.P., and Bernstein D.S. Finite-time stability of continuous autonomous systems. SIAM Journal on Control and Optimization 38 3 (2000) 751-766
4. Clarke F.H. Optimization and nonsmooth analysis. Canadian mathematical society series of monographs and advanced texts (1983), Wiley, New York ISBN 047187504X
5. Clarke, F. H. (2004). Lyapunov functions and feedback in nonlinear control. In M. S. de Queiroz, M. Malisoff, P. Wolenski (Eds.), Optimal control, stabilization and nonsmooth analysis. Lecture notes in control and information sciences (Vol. 301, pp. 267-282). New York: Springer.
6. Clarke F.H., Ledyaev Y., Rifford L., and Stern R. Feedback stabilization and Lyapunov functions. SIAM Journal on Control and Optimization 39 (2000) 25-48
7. Coron J.M. On the stabilization in finite time of locally controllable systems by means of continuous time-varying feedback laws. SIAM Journal on Control and Optimization 33 (1995) 804-833
8. Cortés J., and Bullo F. Coordination and geometric optimization via distributed dynamical systems. SIAM Journal on Control and Optimization 44 5 (2005) 1543-1574
9. Cortés J., Martínez S., and Bullo F. Spatially-distributed coverage optimization and control with limited-range interactions. ESAIM. Control, Optimisation & Calculus of Variations 11 4 (2005) 691-719
10. Filippov, A. F. (1988). Differential equations with discontinuous righthand sides, Mathematics and its applications. Vol. 18, Dordrecht: Kluwer Academic Publishers. The Netherlands.
11. Gazi V., and Passino K.M. Stability analysis of swarms. IEEE Transactions on Automatic Control 48 4 (2003) 692-697
12. Helmke U., and Moore J.B. Optimization and dynamical systems (1994), Springer, New York ISBN 0387198571
13. Hirsch W.M., and Smale S. Differential equations, dynamical systems and linear algebra (1974), Academic Press, New York
14. Ögren P., Fiorelli E., and Leonard N.E. Cooperative control of mobile sensor networks: Adaptive gradient climbing in a distributed environment. IEEE Transactions on Automatic Control 49 8 (2004) 1292-1302
15. Olfati-Saber, R., Fax, J. A., & Murray, R. M. (submitted). Consensus and cooperation in multi-agent networked systems. Proceedings of the IEEE, submitted for publication.
16. Olfati-Saber R., and Murray R.M. Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control 49 9 (2004) 1520-1533
17. Ren, W., Beard, R. W., & Atkins, E. M. (2005). A survey of consensus problems in multi-agent coordination. In American control conference (pp. 1859-1864), Portland, OR, June 2005.
18. Ryan E.P. Finite-time stabilization of uncertain nonlinear planar systems. Dynamics and Control 1 (1991) 83-94
19. Shevitz D., and Paden B. Lyapunov stability theory of nonsmooth systems. IEEE Transactions on Automatic Control 39 9 (1994) 1910-1914
20. Tanner, H., Jadbabaie, A., & Pappas, G. J. (2003). Stable flocking of mobile agents, Part I: Fixed topology. In IEEE conference on decision and control, (pp. 2010-2015), Maui, HI, December 2003.