On the control of a flock by a leader

Proceedings of the Steklov Institute of Mathematics

Volumn 268, Issue 1, 2010, Pages 49-57

  Brockett, R W ^a  

^a HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77952278197     PISSN: 00815438     EISSN: None     Source Type: Journal    
DOI: 10.1134/S0081543810010050     Document Type: Article

References (9)

1. C. W. Reynolds, "Flocks, Herds, and Schools: A Distributed Behavioral Model," Computer Graphics 21(4), 25-34 (1987) (SIGGRAPH'87 Conf. Proc.).
2. R. W. Brockett, "Optimal Control of the Liouville Equation," in Proc. Int. Conf. on Complex Geometry and Related Fields, Ed. by Zhijie Chen et al. (Am. Math. Soc., Providence, RI, 2007), pp. 23-35.
3. T. Eren, P. N. Belhumeur, and A. S. Morse, "Closing Ranks in Vehicle Formations Based on Rigidity," in Proc. 41st IEEE Conf. on Decision and Control (IEEE Press, Piscataway, 2002), Vol. 3, pp. 2959-2964.
4. R. Olfati-Saber and R. M. Murray, "Graph Rigidity and Distributed Formation Stabilization of Multi-vehicle Systems," in Proc. 41st IEEE Conf. on Decision and Control (IEEE Press, Piscataway, 2002), Vol. 3, pp. 2965-2971.
5. T. Eren, D. K. Goldenberg, W. Whitley, Y. R. Yang, A. S. Morse, B. D. O. Anderson, and P. N. Belhumeur, "Rigidity, Computation, and Randomization in Network Localization," in Proc. INFOCOM 2004: 23rd Annual Joint Conf. IEEE Computer and Commun. Soc., Hong Kong, China, Mar. 2004 (IEEE Press, Piscataway, 2004), Vol. 4, pp. 2673-2684.
6. R. W. Brockett, "The Global Description of Locally Linear Systems," in Feedback Control of Linear and Nonlinear Systems, Ed. by D. Hinrichsen and A. Isidori (Springer, New York, 1982), Lect. Notes Control Inf. Sci. 39, pp. 1-8.
7. N. N. Krasovskii, Some Problems of the Theory of Stability of Motion (Fizmatgiz, Moscow, 1959). Engl. transl.: N. N. Krasovskii, Stability of Motion. Applications of Lyapunov's Second Method to Differential Systems and Equations with Delay (Stanford Univ. Press, Stanford, CA, 1963).
8. J. P. LaSalle, "Some Extensions of Liapunov's Second Method," IRE Trans. Circuit Theory CT-7, 520-527 (1960).
9. J. L. Massera, "On Liapounoff's Conditions of Stability," Ann. Math., Ser. 2, 50, 705-721 (1949).