Spatially-distributed coverage optimization and control with limited-range interactions

ESAIM - Control, Optimisation and Calculus of Variations

Volumn 11, Issue 4, 2005, Pages 691-719

  Cortés, Jorge ^a   Martínez, Sonia ^b   Bullo, Francesco ^b  

^a Santa Cruz   (United States)

^b University of California at Santa Barbara   (United States)

Author keywords

Coordination and cooperative control; Distributed dynamical systems; Geometric optimization; Nonsmooth analysis; Voronoi partitions

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; CONSTRAINT THEORY; CONVERGENCE OF NUMERICAL METHODS; DISCRETE TIME CONTROL SYSTEMS; MATHEMATICAL MODELS; OPTIMIZATION; PROXIMITY INDICATORS;

COORDINATION AND COOPERATIVE CONTROL; DISTRIBUTED DYNAMICAL SYSTEMS; GEOMETRIC OPTIMIZATION; NONSMOOTH ANALYSIS; VORONOI PARTITIONS;

DISTRIBUTED PARAMETER CONTROL SYSTEMS;

EID: 30844447688     PISSN: 12928119     EISSN: 12623377     Source Type: Journal    
DOI: 10.1051/cocv:2005024     Document Type: Article

References (30)

1. R.C. Arkin, Behavior-Based Robotics. Cambridge, Cambridge University Press (1998).
2. Y. Asami, A note on the derivation of the first and second derivative of objective functions in geographical optimization problems. J. Faculty Engineering, The University of Tokio (B) 41 (1991) 1-13.
3. R.G. Bartle, The Elements of Integration and Lebesgue Measure, 1st edn. Wiley-Interscience (1995).
4. M. de Berg, M. van Kreveld and M. Overmars, Computational Geometry: Algorithms and Applications. New York, SpringerVerlag (1997).
5. S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, Cambridge University Press (2004).
6. A.J. Chorin and J.E. Marsden, A Mathematical Introduction to Fluid Mechanics. 3rd edn., Ser. Texts in Applied Mathematics. New York, Springer-Verlag 4 (1994).
7. J. Cortes and F. Bullo, Coordination and geometric optimization via distributed dynamical systems. SIAM J. Control Optim. (June 2004), to appear.
8. J. Cortes, S. Martinez, T. Karatas and F. Bullo, Coverage control for mobile sensing networks. IEEE Trans. Robotics Automat. 20 (2004) 243-255.
9. R. Diestel, Graph Theory. 2nd edn., Ser. Graduate Texts in Mathematics. New York, Springer-Verlag 173 (2000).
10. Z. Drezner and H.W. Hamacher, Eds., Facility Location: Applications and Theory. New York, Springer-Verlag (2001).
11. Q. Du, V. Faber and M. Gunzburger, Centroidal Voronoi tessellations: applications and algorithms. SIAM Rev. 41 (1999) 637-676.
12. H. Edelsbrunner and N.R. Shah, Triangulating topological spaces. Internat. J. Comput. Geom. Appl. 7 (1997) 365-378.
13. J. Gao, L.J. Guibas, J. Hershberger, L. Zhang and A. Zhu, Geometric spanner for routing in mobile networks, in ACM International Symposium on Mobile Ad-Hoc Networking & Computing (MobiHoc). Long Beach, CA (Oct. 2001) 45-55.
14. R.M. Gray and D.L. Neuhoff, Quantization. IEEE Trans. Inform. Theory 44 (1998) 2325-2383. Commemorative Issue 1948-1998.
15. U. Helmke and J. Moore, Optimization and Dynamical Systems. New York, Springer-Verlag (1994).
16. A. Jadbabaie, J. Lin and A.S. Morse, Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. Automat. Control 48 (2003) 988-1001.
17. J.W. Jaromczyk and G.T. Toussaint, Relative neighborhood graphs and their relatives. Proc. of the IEEE 80 (1992) 1502-1517.
18. H.K. Khalil, Nonlinear Systems. Englewood Cliffs, Prentice Hall (1995).
19. J.P. LaSalle, The Stability and Control of Discrete Processes. Ser. Applied Mathematical Sciences. New York, Springer-Verlag 62 (1986).
20. X.-Y. Li, Algorithmic, geometric and graphs issues in wireless networks. Wireless Communications and Mobile Computing 3 (2003) 119-140.
21. D.G. Luenberger, Linear and Nonlinear Programming. Reading, Addison-Wesley (1984).
22. J. Marshall, M. Broucke and B. Francis, Formations of vehicles in cyclic pursuit. IEEE Trans. Automat. Control 49 (2004) 1963-1974.
23. A. Okabe, B. Boots, K. Sugihara and S.N. Chiu, Spatial Tessellations: Concepts and Applications of Voronoi Diagrams. 2nd edn., Ser. Wiley Series in Probability and Statistics. New York, John Wiley & Sons (2000).
24. A. Okabe and A. Suzuki, Locational optimization problems solved through Voronoi diagrams. European J. Oper. Res. 98 (1997) 445-56.
25. A. Okubo, Dynamical aspects of animal grouping: swarms, schools, flocks and herds. Adv. Biophysics 22 (1986) 1-94.
26. R. Olfati-Saber and R.M. Murray, Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Automat. Control 49 (2004) 1520-1533.
27. K.M. Passino, Biomimicry for Optimization, Control, and Automation. New York, Springer-Verlag (2004).
28. C.W. Reynolds, Flocks, herds, and schools: A distributed behavioral model. Computer Graphics 21 (1987) 25-34.
29. K. Rose, Deterministic annealing for clustering, compression, classification, regression, and related optimization problems. Proc. of the IEEE 80 (1998) 2210-2239.
30. A.R. Teel, Nonlinear systems: discrete-time stability analysis. Lecture Notes, University of California at Santa Barbara (2004).