Leader-follower Cucker-Smale type flocking synthesized via mean field Stochastic Control theory

Advances in Intelligent and Soft Computing

Volumn 83, Issue , 2010, Pages 283-298

  Nourian, Mojtaba ^a   Caines, Peter E ^a   Malhamé, Roland P ^b   Huang, Minyi ^c  

^a MCGILL UNIVERSITY   (Canada)

^b GERAD   (Canada)

^c CARLETON UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL LAWS; DETERMINISTIC EQUATIONS; DYNAMIC GAME; EQUATION SYSTEMS; EXISTENCE OF UNIQUE SOLUTION; FLOCKING ALGORITHMS; LARGE POPULATION; LEADER-FOLLOWER; LINEAR COUPLING; LINEAR QUADRATIC GAUSSIAN; MEAN FIELD; NASH EQUILIBRIUM; NON-LINEAR DYNAMICS; POPULATION SIZES; REFERENCE VELOCITY; STOCHASTIC CONTROL; STOCHASTIC CONTROL THEORY; SYSTEM OF EQUATIONS; SYSTEMS OF EQUATIONS; WEIGHTED AVERAGES;

CONTROL THEORY; COST FUNCTIONS; COUPLINGS; GAME THEORY; MULTI AGENT SYSTEMS; NONLINEAR EQUATIONS; POPULATION STATISTICS; STOCHASTIC CONTROL SYSTEMS; STOCHASTIC SYSTEMS; VELOCITY;

STOCHASTIC MODELS;

EID: 80052932467     PISSN: 18675662     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-642-16259-6_22     Document Type: Conference Paper

References (30)

1. Reynolds, C.W.: Flocks, herds, and schools: A distributed behavioral model. Computer Graphics 21(4), 25-34 (1987)
2. Perea, L., Gómez, G., Elosegui, P.: Extension of the Cucker-Smale control law to space flight formations. Journal of Guidance, Control, and Dynamics 32(2), 297-325 (2009)
3. Vicsek, T., Czirók, A., Jacob, E.B., Cohen, I., Shochet, O.: Novel type of phase transition in a system of self-driven particles. Phys. Rev. Lett. 75(6), 1226-1229 (1995)
4. Cucker, F., Smale, S.: Emergent behavior in flocks. IEEE Transactions on Automatic Control 52(5), 852-862 (2007) (Pubitemid 46796070)
5. Carrillo, J.A., Fornasier, M., Toscani, G., Vecil, F.: Particle, kinetic, and hydrodynamic models of swarming (preprint 2009)
6. Topaz, C.M., Bertozzi, A.L.: Swarming patterns in a two-dimensional kinematic model for biological groups. SIAM Journal on Applied Mathematics 65(1), 152-174 (2004)
7. Ha, S.Y., Liu, J.G.: A simple proof of the Cucker-Smale flocking dynamics and meanfield limit. Communications in Mathematical Sciences 7(2) (2009)
8. Carrillo, J.A., Fornasier, M., Rosado, J., Toscani, G.: Asymptotic flocking dynamics for the kinetic Cucker-Smale model. SIAM Journal on Mathematical Analysis 42, 218 (2010)
9. Dyer, J.R.G., Johansson, A., Helbing, D., Couzin, I.D., Krause, J.: Leadership, consensus decision making and collective behaviour in humans. Philosophical Transactions of the Royal Society B: Biological Sciences 364(1518), 781-789 (2009)
10. Couzin, I.D., Krause, J., Franks, N.R., Levin, S.A.: Effective leadership and decisionmaking in animal groups on the move. Nature 433(7025), 513-516 (2005) (Pubitemid 40204306)
11. Simaan, M., Cruz, J.B.: On the Stackelberg strategy in nonzero-sum games. Journal of Optimization Theory and Applications 11(5), 533-555 (1973)
12. Gu, D., Wang, Z.: Leader-follower flocking: Algorithms and experiments. IEEE Transactions on Control Systems Technology 17(5), 1211 (2009)
13. Shen, J.: Cucker-Smale flocking under hierarchical leadership. SIAMJournal on Applied Mathematics 68(3), 694-719 (2008)
14. Nagy, M., Ákos, Z., Biro, D., Vicsek, T.: Hierarchical group dynamics in pigeon flocks. Nature 464(7290), 890-893 (2010)
15. Caines, P.E.: Bode lecture: Mean field stochastic control. In: The 48th IEEE Conference on Decision and Control, Shanghai, China (December 2009), http: //www. ieeecss.org/CAB/conferences/cdc2009/shanghai2009.31.pdf
16. Huang, M., Malhamé, R.P., Caines, P.E.: Individual and mass behaviour in large population stochastic wireless power control problems: Centralized and Nash equilibrium solutions. In: 42th IEEE Conference on Decision and Control, Hawaii, pp. 98-103 (December 2003)
17. Huang, M., Caines, P.E., Malhamé, R.P.: The NCE (Mean Field) principle with locality dependent cost interactions. IEEE Transactions on Automatic Control (December 2010)
18. Huang, M., Caines, P.E., Malhamé, R.P.: Large-population cost-coupled LQG problems with nonuniform agents: Individual-mass behavior and decentralized å -Nash equilibria. IEEE Transactions on Automatic Control 52(9), 1560-1571 (2007) (Pubitemid 47456068)
19. Li, T., Zhang, J.F.: Asymptotically optimal decentralized control for large population stochastic multiagent systems. IEEE Transactions on Automatic Control 53(7), 1643-1660 (2008)
20. Nourian, M., Caines, P.E., Malhamé, R.P., Huang, M.: Derivation of consensus algorithm dynamics from mean-field stochastic control NCE equations. In: Proc. of 1st IFAC Workshop on Estimation and Control of Networked Systems (NecSys 2009), Venice, Italy (September 2009), http://www.ifac-papersonline.net/ Detailed/40520.html.
21. Nourian, M., Caines, P.E.,Malhamé, R.P., Huang, M.: A solution to the consensus problem via stochastic mean field control. In: Proc. of 2st IFACWorkshop on Estimation and Control of Networked Systems (NecSys 2010), Annency, France (September 2010)
22. Nourian, M., Caines, P.E.,Malhamé, R.P., Huang, M.: A game theoretic analysis of large population consensus problem via stochastic mean field control theory. IEEE Transactions on Automatic Control (submitted)
23. Huang, M., Malhamé, R.P., Caines, P.E.: Nash certainty equivalence in large population stochastic dynamic games: Connections with the physics of interacting particle systems. In: Proc. of the 45th IEEE Conference on Decision and Control, San Diego, USA, pp. 4921-4926 (December 2006) (Pubitemid 351283806)
24. Huang, M., Malhamé, R.P., Caines, P.E.: Large population stochastic dynamic games: Closed-loop Mckean-Vlasov systems and the Nash certainty equivalence principle. Communications in Information and Systems 6(3), 221-252 (2006)
25. Yin, H.,Mehta, P.G., Meyn, S.P., Shanbhag, U.V.: Synchronization of coupled oscillators is a game. In: American Control Conference (June 2010)
26. Nourian, M., Malhamé, R.P., Huang, M., Caines, P.E.: Mean field (NCE) formulation of estimation based leader-follower collective dynamics. International Journal of Robotics and Automation, Special Issue on New Advances in Nonlinear and Optimal Controls of Robotic and Autonomous Systems (to appear)
27. Nourian, M., Malhamé, R.P., Huang, M., Caines, P.E.: Optimality of adaption based Mean Field (NCE) control laws in Leader-Follower stochastic dynamic games. In: 49th IEEE Conference on Decision and Control, Atlanta, Georgia (December 2010)
28. Nourian, M., Caines, P.E., Malhamé, R.P., Huang, M.: Adaptive mean field control in leader-follower stochastic dynamic games. IEEE Transactions on Automatic Control (submitted)
29. Nourian, M., Caines, P.E., Malhamé, R.P.: Synthesis of Cucker-Smale type flocking via mean field stochastic control theory: Nash equilibria. In: Proc. the 48th Allerton Conference on Communication, Control and Computing, Monticello, Illinois (September 2010)
30. Nourian, M., Caines, P.E., Malhamé, R.P., Huang, M.: Synthesis of Cucker-Smale type flocking via mean field stochastic control theory. Technical Report, McGill Uni. (August 2010)