From geometric optimization and nonsmooth analysis to distributed coordination algorithms

Proceedings of the IEEE Conference on Decision and Control

Volumn 4, Issue , 2003, Pages 3274-3280

  Corté, Jorge ^a   Bullo, Francesco ^a  

^a University of Illinois at Urbana Champaign   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL GEOMETRY; CONTROL SYSTEMS; DYNAMICS; FAILURE ANALYSIS; GRADIENT METHODS; OPTIMIZATION; TOPOLOGY;

MULTI-CENTERED FUNCTIONS; POLYGONS;

ROBOTS;

EID: 1542379751     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2003.1271648     Document Type: Conference Paper

References (17)

1. F. H. Clarke, Optimization and Nonsmooth Analysis, ser. Canadian Mathematical Society Series of Monographs and Advanced Texts. John Wiley & Sons, 1983.
2. R. W. Brockelt, "Dynamical systems that sort lists, diagonalize matrices, and solve linear programming problems," Linear Algebra and its Applications, vol. 146, pp. 79-91, 1991.
3. U. Helmke and J. Moore, Optimization and Dynamical Systems. New York, NY: Springer Verlag, 1994.
4. A. F. Filippov, Differential Equations with Discontinuous Righthand Sides, ser. Mathematics and Its Applications, Dordrecht, The Netherlands: Kluwer Academic Publishers, 1988, vol. 18, original Russian edition: Differentsial'nye Uravneniya s Razryvnoi Pravoi Chast'yu, Nauka, Moscow, 1985.
5. A. F. Filippov, Differential Equations with Discontinuous Righthand Sides, ser. Mathematics and Its Applications, Dordrecht, The Netherlands: Kluwer Academic Publishers, 1988, vol. 18, original Russian edition: Differentsial'nye Uravneniya s Razryvnoi Pravoi Chast'yu, Nauka, Moscow, 1985.
6. 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.
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. S. P. Lloyd, "Least squares quantization in PCM," IEEE Transactions on Information Theory, vol. 28, no. 2, pp. 129-137, 1982, presented as Bell Laboratory Technical Memorandum at a 1957 Institute for Mathematical Statistics meeting.
9. R. M. Gray and D. L. Neuhoff, "Quantization," IEEE Transactions on Information Theory, vol. 44, no. 6, pp. 2325-2383, 1998, commemorative Issue 1948-1998.
10. Q. Du, V. Faber, and M. Gunzburger, "Centroidal Voronoi tessellations: applications and algorithms," SIAM Review, vol. 41, no. 4, pp. 637-676, 1999.
11. J. Cortés and F. Bullo, "Coordination and geometric optimization via distributed dynamical systems," SIAM Journal on Control and Optimization, May 2003, submitted.
12. A. Suzuki and Z. Drezner, "The p-center location problem in an area," Location Science, vol. 4, no. 1/2, pp. 69-82, 1996.
13. Z. Drezner, Ed., Facility Location: A Survey of Applications and Methods, ser. Springer Series in Operations Research. New York, NY: Springer Verlag, 1995.
14. M. de Berg, M. van Kreveld, and M. Overmars, Computational Geometry: Algorithms and Applications. New York, NY: Springer Verlag, 1997.
15. A. Okabe, B. Boots, K. Sugihara, and S. N. Chiu, Spatial Tessellations: Concepts and Applications of Voronoi Diagrams, 2nd ed., ser. Wiley Series in Probability and Statistics. New York, NY: John Wiley & Sons, 2000.
16. J. Cortés, S. Martínez, T. Karatas, and F. Bullo, "Coverage control for mobile sensing networks," IEEE Transactions on Robotics and Automation, Nov. 2002, conditionally accepted.
17. S. Boyd and L. Vandenberghe, "Convex optimization," Dec. 2002, preprint.