On state-dependent dynamic graphs and their controllability properties

IEEE Transactions on Automatic Control

Volumn 50, Issue 3, 2005, Pages 387-392

  Mesbahi, Mehran ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

Dynamic graphs; Graph controllability; State dependent graphs; Szemer di's regularity

Indexed keywords

ALGORITHMS; CONTROL THEORY; CONTROLLABILITY; GRAPH THEORY; SYSTEM THEORY;

DYNAMIC GRAPHS; GRAPH CONTROLLABILITY; STATE DEPENDENT GRAPHS; SZEMEREDI REGULARITY;

DISTRIBUTED PARAMETER CONTROL SYSTEMS;

EID: 16244402704     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2005.843858     Document Type: Article

References (20)

1. M. A. Aizerman, L. A. Gusev, S. V. Petrov, I. M. Smirnova, and L. A. Tenenbaum, "Dynamic approach to analysis of structures described by graphs (foundations of graph-dynamics)," in Topics in the General Theory of Structures, E. R. Caianiello and M. A. Aizerman, Eds. Dordrecht, The Netherlands: D. Reidel, 1987.
2. R. W. Beard, J. Lawton, and F. Y. Hadaegh, "A coordination architecture for spacecraft formation control," IEEE Trans. Control Syst. Technol., vol. 6, no. 9, pp. 777-790, Sep. 1998.
3. B. Bollobás, Combinatorics: Set Systems, Hypergraphs, Families of Vectors, and Combinatorial Probability. Cambridge, U.K.: Cambridge Univ. Press, 1986.
4. B. Bollobás, Modern Graph Theory. New York: Springer-Verlag, 1998.
5. S. P. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM, 1994.
6. R. Diestel, Graph Theory. New York: Springer-Verlag, 2000.
7. P. Erdös and P. Turán, "On some sequences of integers," J. London Math. Soc., vol. 11, pp. 261-264, 1936.
8. J. A. Fax and R. M. Murray, "Information flow and cooperative control of vehicle formations," IEEE Trans. Autom. Control, vol. 49, no. 9, pp. 1465-1476, Sep. 2004.
9. C. Godsil and G. Royle, Algebraic Graph Theory. New York: Springer-Verlag, 2001.
10. R. L. Graham, M. Grötschel, and L. Lovász, Handbook of Combinatorics. Cambridge, MA: MIT Press, 1995.
11. A. Jadbabaie, J. Lin, and A. S. Morse, "Coordination of groups of mobile autonomous agents using nearest neighbor roles," IEEE Trans. Autom. Control, vol. 48, no. 6, pp. 988-1001, Jun. 2003.
12. J. Komlós and M. Simonovits, "Szemerédi's regularity lemma and its applications in graph theory," in Combinatorics: Paul Erdös is Eighty. Budapest, Hungary: Bolyai Soc. Math. Stud., 1996, vol. 2, pp. 295-352.
13. M. Mesbahi and F. Y. Hadaegh, "Formation flying control of multiple spacecraft via graphs, matrix inequalities, and switching," AIAA J. Guid., Control, Dyna., vol. 2, no. 24, pp. 369-377, 2001.
14. M. Mesbahi, "On a dynamic extension of the theory of graphs," in Proc. American Control Conference, June 2002, pp. 1234-1239.
15. R. Olfati-Saber and R. M. Murray, "Consensus problems in networks of agents with switching topology and time-delays," IEEE Trans. Autom. Control, vol. 49, no. 9, pp. 1520-1533, Sep. 2004.
16. S. V. Petrov, "Graph grammars and graphodynamics problem," Autom. Remote Control, vol. 10, pp. 133-138, 1977.
17. E. Prisner, Graph Dynamics. Harlow, U.K.: Longman House, 1995.
18. Handbook of Graph Grammars and Computing by Graph Transformation, G. Rozenberg, Ed., World Scientific, Singapore, 1997.
19. http://planetquest.jpl.nasa.gov/TPF/tpf_index.html [Online]
20. H. Whitney, "Congruent graphs and the connectivity of graphs," Amer. J. Math., vol. 54, pp. 150-168, 1932.