Inverse optimality of cooperative control for networked systems

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2009, Pages 1651-1658

  Qu, Zhihua ^a   Simaan, Marwan ^a  

^a University of Central Florida   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

INVERSE PROBLEMS; MATRIX ALGEBRA; NETWORKED CONTROL SYSTEMS; STOCHASTIC SYSTEMS; TOPOLOGY; TREES (MATHEMATICS);

ASYMPTOTICALLY STABLE; CO-OPERATIVE CONTROL; CO-OPERATIVE SYSTEMS; GLOBALLY REACHABLE NODE; INVERSE-OPTIMAL CONTROL; OPTIMAL PERFORMANCE; QUADRATIC PERFORMANCE INDICES; STOCHASTIC NETWORKS;

FEEDBACK;

EID: 77950789573     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2009.5399741     Document Type: Conference Paper

References (40)

1. A. E. Bryson and Y. C. Ho, Applied Optimal Control. Bristol,PA: Hemisphere Publishing Corp., 1975.
2. J. Cortes, S. Martinez, and F. Bullo, "Robust rendezvous for mobile autonomous agents via proximity graphs in arbitrary dimensions," IEEE Transactions on Automatic Control, vol.51, pp. 1289-1298, 2006.
3. J. B. Cruz, M. Simaan, A. Gacic, and Y. Liu, "Moving horizon game theoretic approaches for control strategies in a military operation," in Proceedings of the 40th IEEE Conference on Decision and Control, Orlando, Florida, December 2001, pp. 628-633.
4. J. A. Fax and R. M. Murray, "Information flow and cooperative control of vehicle formations," IEEE Transactions on Automatic Control, vol.49, pp. 1465-1476, 2004.
5. R. A. Freeman and P. V. Kokotovic, "Inverse optimality in robust stabilization," SIAM Journal on Control and Optimization, vol.34, pp. 1365-1391, 1996.
6. -, Robust nonlinear control design: state-space and Lyapunov techniques. Boston, MA: Birkhauser, 1996.
7. F. R. Gantmacher, The Theory of Matrices, vol.II. New York, NY: Chelsea, 1959.
8. D. H. Jacobson, Extensions of Linear Quadratic Control, Optimization and Matrix Theory. New York, NY: Academic Press, 1977.
9. -, "On the values and strategies for inifinite-time linear quadratic games," IEEE Transactions on Automatic Control, pp. 490-491, 1977.
10. A. Jadbabaie, J. Lin, and A. Morse, "Coordination of groups of mobile autonomous agents using nearest neighbor rules," IEEE Transactions on Automatic Control, vol.48, pp. 988-1001, 2003.
11. R. E. Kalman, "When is a linear control system optimal?" Transactions of the ASME, Journal of Basic Engineering, vol.86, pp. 1-10, 1964.
12. H. K. Khalil, Nonlinear Systems. Upper Saddle River, NJ: Prentice Hall, 3rd ed., 2003.
13. M. Krstic, I. Kanellakopoulos, and P. V. Kokotovic, Nonlinear and Adaptive Control Design. New York: Wiley, 1995.
14. M. Krstic and Z. Li, "Inverse optimal design of input-to-state stabilizing nonlinear systems," IEEE Transactions on Automatic Control, vol.43, pp. 336-350, 1998.
15. F. Lewis and V. L. Syrmos, Optimal Control. John Wiley and Sons, 1995.
16. Z. Lin, M. Brouchke, and B. Francis, "Local control strategies for groups of mobile autonomous agents," IEEE Transactions on Automatic Control, vol.49, pp. 622-629, 2004.
17. Z. Lin, B. Francis, and M. Maggiore, "Necessary and sufficient graphical conditions for formation control of unicycles," IEEE Transactions on Automatic Control, vol.50, pp. 121-127, 2005.
18. -, "State agreement for continuous-time coupled nonlinear systems," SIAM Journal on Control and Optimization, vol.46, pp. 288-307, 2007.
19. Y. Liu, M. Simaan, and J. B. Cruz, "Game theoretic approach to cooperative teaming and tasking in the presence of an adversary," in Proceedings of the American Control Conference, Denver, Colorado, June 2003, pp. 5375-5380.
20. H. Minc, Nonnegative Matrices. New York: John Wiley & Sons, 1988.
21. L. Moreau, "Stability of multiagent systems with time-dependent communication links," IEEE Transactions on Automatic Control, vol.50, pp. 169-182, 2005.
22. O. Perron, "Zur theorie der matrizen," The Mathematische Annalen, vol.64, pp. 248-263, 1907.
23. Z. Qu, Robust Control of Nonlinear Uncertain Systems. New York: Wiley Interscience, 1998.
24. -, "A comparison theorem for cooperative control of nonlinear systems," in Proceedings of American Control Conference, Seattle, Washington, June 2008.
25. -, Cooperative Control of Dynamical Systems. London: Springer Verlag, 2009.
26. Z. Qu, J. Wang, and J. Chunyu, "Lyapunov design of cooperative control and its application to the consensus problem," in Proceedings of IEEE Multi-conference on Systems and Control, Singapore, October 2007.
27. Z. Qu, J. Wang, and R. A. Hull, "Products of row stochastic matrices and their applications to cooperative control for autonomous mobile robots," in Proceedings of American Control Conference, Portland, Oregon, June 2005.
28. -, "Cooperative control of dynamical systems with application to autonomous vehicles," IEEE Transactions on Automatic Control, vol.53, pp. 894-911, 2008.
29. M. W. Reinsch, "A simple expression for the terms in the bakercampbell-hausdorff series," Journal of Mathematical Physics, vol.41, pp. 2434-2442, 2000.
30. W. Ren and R. W. Beard, "Consensus seeking in multiagent systems under dynamically changing interaction topologies," IEEE Transactions on Automatic Control, vol.50, pp. 655-661, 2005.
31. C. W. Reynolds, "Flocks, herds, and schools: a distributed behavioral model," Computer Graphics (ACM SIGGRAPH 87 Conference Proceedings), vol.21, pp. 25-34, 1987.
32. R. O. Saber and R. M. Murray, "Consensus problems in networks of agents with switching topology and time-delays," IEEE Transactions on Automatic Control, vol.49, pp. 1520-1533, 2004.
33. D. D. Siljak, "Connective stability of competitive equilibrium," Automatica, vol.11, pp. 389-400, 1975.
34. -, Decentralized Control of Complex Systems. Academic press, 1991.
35. M. Simaan and J. B. Cruz, "On the stackelberg strategy in a nonzerosum games," Journal of Optimization Theory and Applications, vol.11, pp. 533-555, 1973.
36. -, "A stackelberg solution for games with many players," IEEE Transactions on Automatic Control, vol.18, pp. 322-324, 1973.
37. E. D. Sontag, "A universal construction of artstein's theorem on nonlinear stabilization," System & Control Letters, vol.13, pp. 117-123, 1989.
38. H. G. Tanner, A. Jadbabaie, and G. J. Pappas, "Stable flocking of mobile agents, part i: fixed topology," in Proceedings of IEEE Conference on Decision and Control, Maui, Hawaii, 2003, pp. 2010-2015.
39. -, "Stable flocking of mobile agents, part ii: dynamic topology," in Proceedings of IEEE Conference on Decision and Control, Maui, Hawaii, 2003, pp. 2016-2021.
40. T. Vicsek, A. Czirok, E. B. Jacob, I. Cohen, and O. Shochet, "Novel type of phase transition in a system of self-driven particles," Physical Review Letters, vol.75, pp. 1226-1229, 1995.