Mean field games for large-population multiagent systems with Markov jump parameters

SIAM Journal on Control and Optimization

Volumn 50, Issue 4, 2012, Pages 2308-2334

  Wang, Bing Chang ^a   Zhang, Ji Feng ^a  

^a INSTITUTE OF SYSTEMS SCIENCE   (China)

Author keywords

Distributed game; Markov jump parameter; Mean field approach; Multiagent system; Optimal control

Indexed keywords

ASYMPTOTICALLY OPTIMAL; DETERMINISTIC QUANTITY; DISTRIBUTED GAME; DISTRIBUTED STRATEGIES; MARKOV JUMP PARAMETER; MARKOV JUMPS; MEAN FIELD; MEAN FIELD APPROACH; MEAN-FIELD COUPLING; NASH EQUILIBRIA; NONLINEAR TERMS; NUMERICAL EXAMPLE; OPTIMAL CONTROLS; PARAMETER JUMP; REFERENCE SIGNALS; STACKELBERG EQUILIBRIUM; STRUCTURE PARAMETER; TIME VARYING PARAMETER; TRACKING PROBLEM; TWO-PLAYER GAMES;

CLOSED LOOP SYSTEMS; ELECTRIC SHIP EQUIPMENT; GAME THEORY; MARKOV PROCESSES;

MULTI AGENT SYSTEMS;

EID: 84865013442     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/100800324     Document Type: Article

References (38)

1. T. Basar and G. J. Olsder, Dynamic Noncooperative Game Theory, Academic Press, London, 1982.
2. C. T. Bauch and D. J. D. Earn, Vaccination and the theory of games, Proc. Natl. Acad. Sci. USA, 101 (2004), pp. 13391-13394.
3. D. Bauso, L. Giarré, and R. Pesenti, Non-linear protocols for optimal distributed consensus in networks of dynamics agents, Systems Control Lett., 55 (2006), pp. 918-928.
4. J. D. Birdwell, On reliable control systems design, PhD dissertation, Electronic Systems Laboratory, Massachusetts Institute of Technology, report ESL-TH-821, 1978.
5. P. E. Caines, Mean field stochastic control, in Proceedings of the 48th IEEE Conference on Decision and Control, Shanghai, China, 2009; also available online from http://www. cim.mcgill.ca/~arman/Shanghai2009/Shanghai2009.pdf.
6. C. Y. Chong, S. P. Kumar, and B. A. Hamilton, Sensor networks: Evolution, opportunities, and challenges, Proc. IEEE, 91 (2003), pp. 1247-1256.
7. O. L. V. Costa, M. D. Fragoso, and R. P. Marques, Discrete-Time Markov Jump Linear Systems, Springer-Verlag, London, 2005.
8. F. Cucker and S. Smale, Emergent behavior in flocks, IEEE Trans. Automat. Control, 52 (2007), pp. 852-862.
9. G. M. Erickson, Differential game models of advertising competition, European J. Oper. Res., 83 (1995), pp. 431-438.
10. G. M. Erickson, An oligopoly model of dynamic advertising competition, European J. Oper. Res., 197 (2009), pp. 374-388.
11. Y. Fang and K. A. Loparo, Stabilization of continuous-time jump linear systems, IEEE Trans. Automat. Control, 47 (2002), pp. 1590-1603.
12. M. K. Ghosh, A. Arapostathis, and S. I. Marcus, Ergodic control of switching diffusions, SIAM J. Control Optim., 35 (1997), pp. 1952-1988.
13. D. Gröbaum and A. Okubo, Modeling social animal aggregations, in Frontiers in Theoretical Biology, Lecture Notes in Biomathematics 100, Springer-Verlag, New York, 1994, pp. 296- 325.
14. M. Huang, P. E. Caines, and R. P. Malhamé, Individual and mass behaviour in large population stochastic wireless power control problems: Centralized and Nash equilibrium solutions, in Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, HI, 2003, pp. 98-103.
15. M. Huang, P. E. Caines, and R. P. Malhamé, Uplink power adjustment in wireless communication systems: A stochastic control analysis, IEEE Trans. Automat. Control, 49 (2004), pp. 1693-1708.
16. M. Huang, R. P. Malhamé, and P. E. Caines, Nash certainty equivalence in large population stochastic dynamic games: Connections with the physics of interacting particle systems, in Proceedings of the 45th IEEE Conference Decision and Control, San Diego, CA, 2006, pp. 4921-4926.
17. M. Huang, R. P. Malhamé, and P. E. Caines, Large population stochastic dynamic games: Closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle, Commun. Inf. Syst., 6 (2006), pp. 221-251.
18. M. Huang, P. E. Caines, and R. P. Malhamé, Large-population cost coupled LQG problems with nonuniform agents: Individual-mass behavior and decentralized ε-Nash equilibria, IEEE Trans. Automat. Control, 52 (2007), pp. 1560-1571.
19. M. Huang, Large-population LQG games involving a major player: The Nash certainty equivalence principle, SIAM J. Control Optim., 48 (2010), pp. 3318-3353.
20. Y. Ji and H. J. Chizeck, Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control, IEEE Trans. Automat. Control, 35 (1990), pp. 777-788.
21. V. E. Lambson, Self-enforcing collusion in large dynamic markets, J. Econom. Theory, 34 (1984), pp. 282-291.
22. J.-M. Lasry and P.-L. Lions. Jeux à champ moyen. I C Le cas stationnaire, C. R. Math. Acad. Sci. Paris, 343 (2006), pp. 619-625.
23. J.-M. Lasry and P.-L. Lions. Mean field games, Japan. J. Math., 2 (2007), pp. 229-260.
24. T. Li and J. F. Zhang, Asymptotically optimal decentralized control for large population stochastic multi-agent systems, IEEE Trans. Automat. Control, 53 (2008), pp. 1643-1660.
25. T. Li and J. F. Zhang, Decentralized tracking-type games for multi-agent systems with coupled ARX models: Asymptotic Nash equilibria, Automatica J. IFAC, 44 (2008), pp. 713-725.
26. R. S. Lipster and A. N. Shiryaev, Statistics of Random Processes, vol. 3, Springer-Verlag, New York, 1977, pp. 329-340.
27. C. Q. Ma, T. Li, and J. F. Zhang, Linear quadratic decentralized dynamic games for largepopulation discrete-time stochastic multi-agent systems, J. Systems Sci. Math. Sci., 27 (2007), pp. 464-480.
28. M. Mariton, Jump Linear Systems in Automatic Control, Marcel Dekker, New York, 1990.
29. M. Nourian, P. E. Caines, R. P. Malhame, and M. Huang, Mean field LQG control in leader-follower stochastic multi-agent systems: Likelihood ratio based adaptation, IEEE Trans. Automat. Control, 57 (2012), to appear.
30. B. Øksendal, Stochastic Differential Equations. An Introduction with Applications, 6th ed., Springer-Verlag, Berlin, 2003.
31. C. Reynolds, Flocks, herds and schools: A distributed behavior model, Computer Graphics, 21 (1987), pp. 25-34.
32. E. Semsar-Kazerooni and K. Khorasani, Multi-agent team cooperation: A game theory approach, Automatica J. IFAC, 45 (2009), pp. 2205-2213.
33. D. D. Siljak, Dynamic reliability using multiple control systems, in Proceedings of the 2nd Lawerence Symposium on System Decision Sciences, Berkeley, CA, 1978.
34. D. D. Sworder, Feedback control of a class of linear systems with jump parameters, IEEE Trans. Automat. Control, 14 (1969), pp. 9-14.
35. W. M. Wonham, Random differential equations in control theory, Probabilistic Methods in Applied Mathematics 2, A. T. Bharucha-Reid, ed., Academic Press, New York, 1971.
36. G. Y. Weintraub, C. L. Benkard, and B. Van Roy, Oblivious equilibrium: A mean field approximation for large-scale dynamic games, in Advances in Neural Information Processing Systems, MIT Press, Cambridge, MA, 2005.
37. G. Y. Weintraub, C. L. Benkard, and B. Van Roy, Markov perfect industry dynamics with many firms, Econometrica, 76 (2008), pp. 1375-1411.
38. Q. Zhang and J. F. Zhang, Adaptive tracking control for coupled stochastic linear multi-agent systems: Stability, optimality and robustness, IEEE Trans. Automat. Control, submitted.