Potential game design for a class of distributed optimisation problems

Journal of Control and Decision

Volumn 1, Issue 2, 2014, Pages 166-179

  Yi, Peng ^a   Zhang, Yanqiong ^a   Hong, Yiguang ^a  

^a INSTITUTE OF SYSTEMS SCIENCE   (China)

Author keywords

distributed optimisation; multi agent systems; plug in electric vehicle; potential game

Indexed keywords

CONTINUOUS TIME SYSTEMS; DIRECTED GRAPHS; LAGRANGE MULTIPLIERS; MULTI AGENT SYSTEMS; OPTIMIZATION; PLUG-IN ELECTRIC VEHICLES;

COMMUNICATION GRAPHS; CONTINUOUS TIME MODELING; CONVERGENCE AND STABILITY; DISTRIBUTED OPTIMISATION; GAME-BASED APPROACHES; LAGRANGIAN MULTIPLIERS; OPTIMISATION PROBLEMS; POTENTIAL GAMES;

LEARNING ALGORITHMS;

EID: 84919792924     PISSN: 23307706     EISSN: 23307714     Source Type: Journal    
DOI: 10.1080/23307706.2014.899111     Document Type: Article

References (29)

1. Arrow, K. J., Hurwitz, L., & Uzawa, H., (1958). Studies in linear and nonlinear programming. Stanford: Stanford University Press.
2. Basar, T., & Olsder, G. J., (1999). Dynamic noncooperative game theory. Philadelphia, PA: SIAM.
3. Boyd, S., & Vandenberghe, L., (2004). Convex optimization. Cambridge: Cambridge University Press.
4. Campos-Nanez, E., Garcia, A., & Li, C., (2008). A game-theoretic approach to efficient power management in sensor networks. Operations Research, 56(3), 552–561.
5. Duchi, J. C., Agarwal, A., & Wainwright, M. J., (2012). Dual averaging for distributed optimization: convergence analysis and network scaling. IEEE Transactions on Automatic Control, 57(3), 592–606.
6. Fudenberg, D., & Levine, D. K., (1998). The theory of learning in games. Cambridge, MA: MIT Press.
7. Fudenberg, D., & Tirole, J., (1991). Game Theory. Cambridge, MA: MIT Press.
8. Gharesifard, B., & Cortes, J., (2014). Distributed continuous-time convex optimization on weight-balanced digraphs. IEEE Transactions on Automatic Control, 59, 781–786.
9. Godsil, C. D., Royle, G., & Godsil, C. D., (2001). Algebraic graph theory, Vol. 207. New York: Springer.
10. Li, N., & Marden, J. R., (2013). Designing games for distributed optimization. IEEE Journal of Selected Topics in Signal Processing, 7(2), 230–242.
11. Lou, Y., Shi, G., Johansson, K.H., & Hong, Y., (2012). Reaching optimal consensus for multi-agent systems based on approximate projection. The 10th World Congress on Intelligent Control and Automation, 2794-2800.
12. Marden, J. R., (2012). State based potential games. Automatica, 48(12), 3075–3088.
13. Marden, J. R., Arslan, G., & Shamma, J. S., (2009). Cooperative control and potential games. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 39(6), 1393–1407.
14. Monderer, D., & Shapley, L., (1996). Potential games. Games Economic Behaviour, 14(1), 124–143.
15. Nedic, A., & Ozdaglar, A., (2009). Distributed subgradient methods for multi-agent optimization. IEEE Transactions on Automatic Control, 54(1), 48–61.
16. Nedic, A., Ozdaglar, A., & Parrilo, P. A., (2010). Constrained consensus and optimization in multi-agent networks. IEEE Transactions on Automatic Control, 55(4), 922–938.
17. Nisam, N., Roughgarden, T., Tardos, E., & Vazirani, V. V., (2007). Algorithm game theory. Cambridge: Cambridge University Press.
18. Saad, W., Han, Z., Poor, H. V., & Basar, T., (2012). Game-theoretic methods for the smart grid: an overview of microgrid systems, demand-side management, and smart grid communications. Signal Processing Magazine, IEEE, 29(5), 86–105.
19. Shapley, L. S., (1953). Stochastic games. PNAS, 39(10), 1095–1100.
20. Shi, G., & Johansson, K. H., (2013). Robust consensus for continuous-time multi-agent dynamics. SIAM Journal on Control and Optimization, 51(5), 367–3691.
21. Shi, G., Johansson, K. H., & Hong, Y., (2013). Reaching an Optimal Consensus: Dynamical Systems That Compute Intersections of Convex Sets. IEEE Transactions on Automatic Control, 58(3), 610–622.
22. Tsitsiklis, J., & Athans, M., (1984). Convergence and asymptotic agreement in distributed decision problems. IEEE Transactions on Automatic Control, 29(1), 42–50.
23. Wang, J., & Elia, N., (2009a). Distributed agreement in the presence of noise. In 47th Annual Allerton Conference on Communication, Control, and Computing (pp. 1575-1581). Allerton House, IL.
24. Wang, J., & Elia, N., (2009b). Agents design for distributed consensus over networks of fixed and switching topologies. 48th IEEE Conference on Decision and Control held jointly with the 28th Chinese Control Conference. CDC/CCC 2009, 5815-5820. Shanghai, China.
25. Wang, J., & Elia, N., (2010). Control approach to distributed optimization. In Allerton Conference on Communications Control and Computing (pp. 557–561). Allerton House, IL.
26. Wang, J., & Elia, N., (2011). A control perspective for centralized and distributed convex optimization. In 50st IEEE Conferfence on Decision and Control (CDC) (pp. 3800-3805). Orlando, FL.
27. Wei, E., & Ozdaglar, A., (2012). Distributed alternating direction method of multipliers. In 51st IEEE Conference on Decision and Control (CDC) (pp. 5445-5450). Maui, HI.
28. Yi, P., Zhang, Y., & Hong, Y., (2013). Design games to solve distributed optimization problem with application in electric vehicle charge management. In 2013 32nd Chinese Control Conference (CCC), (pp. 6873-6878). Xi’an, China.
29. Young, H. P., (2004). Strategic learning and its limits. Oxford: Oxford University Press.