Robust mean field social control problems with applications in analysis of opinion dynamics

References

• Anderson, B. D. O., & Ye, M. (2019, April). Recent advances in the modelling and analysis of opinion dynamics on influence networks. International Journal of Automation and Computing, 16(2), 129–149. https://doi.org/10.1007/s11633-019-1169-8
   Web of Science ®Google Scholar
• Arabneydi, J., & Aghdam, A. G. (2020, October). Deep teams: Decentralized decision making with finite and infinite number of agents. IEEE Transactions on Automatic Control, 65(10), 4230–4245. https://doi.org/10.1109/TAC.9
   Web of Science ®Google Scholar
• Arabneydi, J., & Mahajan, A. (2016, August). Linear quadratic mean field teams: Optimal and approximately optimal decentralized solutions. Available on arXiv, arXiv:1609.00056.
   Google Scholar
• Arefin, M. R., Masaki, T., Kabir, K. M. A., & Tanimoto, J. (2019, December). Interplay between cost and effectiveness in influenza vaccine uptake: A vaccination game approach. Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 475(2232), 20190608. https://doi.org/10.1098/rspa.2019.0608
   PubMed Web of Science ®Google Scholar
• Başar, T., & Olsder, G. J. (1998). Dynamic noncooperative game theory. Society for Industrial and Applied Mathematics.
   Google Scholar
• Bauso, D., Tembine, H., & Başar, T. (2016, January). Opinion dynamics in social networks through mean-field games. L2-disturbance. SIAM Journal on Control and Optimization, 54(6), 3225–3257. https://doi.org/10.1137/140985676
   Web of Science ®Google Scholar
• Bensoussan, A., Frehse, J., & Yam, P. (2013). Mean field games and mean field type control theory. Springer.
   Google Scholar
• Bensoussan, A., Sung, K. C. J., & Yam, S. C. P. (2013, December). Linear-quadratic time-inconsistent mean field games. Dynamic Games and Applications, 3(4), 537–552. https://doi.org/10.1007/s13235-013-0090-y
   Web of Science ®Google Scholar
• Caines, P. E., & Huang, M. (2019, July). Graphon mean field games and the GMFG equations. In 2018 IEEE conference on decision and control (pp. 4129–4134). IEEE.
   Google Scholar
• Caines, P. E., Huang, M., & Malhamé, R. P. (2017). Mean field games. In T. Basar & G. Zaccour (Eds.), Handbook of dynamic game theory. Spinger.
   Google Scholar
• Carmona, R., & Delarue, F. (2013, January). Probabilistic analysis of mean-field games. SIAM Journal on Control and Optimization, 51(4), 2705–2734. https://doi.org/10.1137/120883499
   Web of Science ®Google Scholar
• Chen, G., Duan, X., Friedkin, N. E., & Bullo, F. (2019, February). Social power dynamics over switching and stochastic influence networks. IEEE Transactions on Automatic Control, 64(2), 582–597. https://doi.org/10.1109/TAC.2018.2822182
   Web of Science ®Google Scholar
• Firoozi, D., Jaimungal, S., & Caines, P. E. (2020, August). Convex analysis for LQG systems with applications to major–minor LQG mean–field game systems. Systems & Control Letters, 142, 104734. https://doi.org/10.1016/j.sysconle.2020.104734
   Web of Science ®Google Scholar
• Friedkin, N. E., Proskurnikov, A. V., Tempo, R., & Parsegov, S. E. (2016, October). Network science on belief system dynamics under logic constraints. Science, 354(6310), 321–326. https://doi.org/10.1126/science.aag2624
   PubMed Web of Science ®Google Scholar
• Gao, S., & Caines, P. E. (2020, October). Graphon control of large-scale networks of linear systems. IEEE Transactions on Automatic Control, 65(10), 4090–4105. https://doi.org/10.1109/TAC.9
   Web of Science ®Google Scholar
• Gao, S., Caines, P. E, & Huang, M. (2020, April). LQG graphon mean field games. Available on arXiv, arXiv:2004.00679.
   Google Scholar
• Gomes, D. A., & Saude, J. (2014, June). Mean field games models: A brief survey. Dynamic Games and Applications, 4(2), 110–154. https://doi.org/10.1007/s13235-013-0099-2
   Web of Science ®Google Scholar
• Ho, Y.-C. (1980, June). Team decision theory and information structures. Proceedings of the IEEE, 68(6), 644–654. https://doi.org/10.1109/PROC.1980.11718
   Web of Science ®Google Scholar
• Huang, J., & Huang, M. (2017, January). Robust mean field linear-quadratic-Gaussian games with unknown L2-disturbance. SIAM Journal on Control and Optimization, 55(5), 2811–2840. https://doi.org/10.1137/15M1014437
   Web of Science ®Google Scholar
• Huang, M. (2010, January). Large-population LQG games involving a major player: The Nash certainty equivalence principle. SIAM Journal on Control and Optimization, 48(5), 3318–3353. https://doi.org/10.1137/080735370
   Web of Science ®Google Scholar
• Huang, M., Caines, P. E., & Malhamé, R. P. (2003, December). Individual and mass behaviour in large population stochastic wireless power control problems: Centralized and Nash equilibrium solutions. In 42nd IEEE international conference on decision and control (pp. 98–103). IEEE.
   Google Scholar
• Huang, M., Caines, P. E., & Malhamé, R. P. (2007, September). Large-population cost-coupled LQG problems with non-uniform agents: Individual-mass behavior and decentralized ϵ-Nash equilibria. IEEE Transactions on Automatic Control, 52(9), 1560–1571. https://doi.org/10.1109/TAC.2007.904450
   Web of Science ®Google Scholar
• Huang, M., Caines, P. E., & Malhamé, R. P. (2012, June). Social optima in mean field LQG control: Centralized and decentralized strategies. IEEE Transactions on Automatic Control, 57(7), 1736–1751. https://doi.org/10.1109/TAC.2012.2183439
   Web of Science ®Google Scholar
• Huang, M., Malhamé, R. P., & Caines, P. E. (2006, July). Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle. Communication in Information and Systems, 6(3), 221–251. https://doi.org/10.4310/CIS.2006.v6.n3.a5
   Google Scholar
• Huang, M., & Nguyen, S. L. (2019, April). Linear-quadratic mean field social optimization with a major player. Available on arXiv, arXiv: 1904.03346.
   Google Scholar
• Huang, M., & Zhou, M. (2020, April). Linear quadratic mean field games: Asymptotic solvability and relation to the fixed point approach. IEEE Transactions on Automatic Control, 65(4), 1397–1412. https://doi.org/10.1109/TAC.9
   Web of Science ®Google Scholar
• Jia, P., Mirtabatabaei, A., Friedkin, N. E., & Bullo, F. (2015, January). Opinion dynamics and the evolution of social power in influence networks. SIAM Review, 57(3), 367–397. https://doi.org/10.1137/130913250
   Web of Science ®Google Scholar
• Larranaga, M., Denis, J., Assaad, M., & Turck, K. D. (2020, January). Energy-efficient distributed transmission scheme for MTC in dense wireless networks: A mean-field approach. IEEE Internet of Things Journal, 7(1), 477–490. https://doi.org/10.1109/JIoT.6488907
   Web of Science ®Google Scholar
• Lasry, J. M., & Lions, P. L. (2007, March). Mean field games. Japanese Journal of Mathematics, 2(1), 229–260. https://doi.org/10.1007/s11537-007-0657-8
   Web of Science ®Google Scholar
• Li, T., & Zhang, J.-F. (2008, September). Asymptotically optimal decentralized control for large population stochastic multiagent systems. IEEE Transactions on Automatic Control, 53(7), 1643–1660. https://doi.org/10.1109/TAC.2008.929370
   Web of Science ®Google Scholar
• Liang, Y., & Wang, B.-C. (2019, July). Robust mean field social optimal control with applications to opinion dynamics. In IEEE 15th international conference on control and automation (pp. 1079–1084). IEEE.
   Google Scholar
• Lovász, L. (2012). Large networks and graph limits (Vol. 60). American Mathematical Society.
   Google Scholar
• Ma, J., & Yong, J. (1999). Forward-backward stochastic differential equations and their applications. Springer.
   Google Scholar
• Moon, J., & Başar, T. (2017, March). Linear quadratic risk-sensitive and robust mean field games. IEEE Transactions on Automatic Control, 62(3), 1062–1077. https://doi.org/10.1109/TAC.2016.2579264
   Web of Science ®Google Scholar
• Mou, L., & Yong, J. (2006, January). Two-person zero-sum linear quadratic stochastic differential games by a Hilbert space method. Journal of Industrial and Management Optimization, 2(1), 95–117. https://doi.org/10.3934/jimo.2006.2.95
   Web of Science ®Google Scholar
• Radner, R. (1962, September). Team decision problems. Annals of Mathematical Statistics, 33(3), 857–881. https://doi.org/10.1214/aoms/1177704455
   Google Scholar
• Thygesen, U. H. (1997). A survey of Lyapunov techniques for stochastic differential equations (IMM Technical Report). Copenhagen: Department of Mathematical Modelling, Technical University of Denmark.
   Google Scholar
• Wang, B.-C., Huang, J., & Zhang, J.-F. (2021, April). Social optima in robust mean field LQG control: From finite to infinite horizon. IEEE Transactions on Automatic Control, 66(4), 1529–1544. https://doi.org/10.1109/TAC.9
   Web of Science ®Google Scholar
• Wang, B.-C., & Huang, M. (2019, February). Mean field production output control with sticky prices: Nash and social solutions. Automatica, 100(6), 90–98. https://doi.org/10.1016/j.automatica.2018.11.006
   Web of Science ®Google Scholar
• Wang, B.-C., & Zhang, J.-F. (2012a, January). Mean field games for large-population multi-agent systems with Markov jump parameters. SIAM Journal on Control and Optimization, 50(4), 2208–2334. https://doi.org/10.1137/100800324
   Web of Science ®Google Scholar
• Wang, B.-C., & Zhang, J.-F. (2012b, September). Distributed control of multi-agent systems with random parameters and a major agent. Automatica, 48(9), 2093–2106. https://doi.org/10.1016/j.automatica.2012.06.050
   Web of Science ®Google Scholar
• Wang, B.-C., & Zhang, J.-F. (2017, January). Social optima in mean field linear-quadratic-Gaussian models with Markov jump parameters. SIAM Journal on Control and Optimization, 55(1), 429–456. https://doi.org/10.1137/15M104178X
   Web of Science ®Google Scholar
• Weintraub, G., Benkard, C., & Roy, B. V. (2008, November). Markov perfect industry dynamics with many firms. Econometrica, 76(6), 1375–1411. https://doi.org/10.3982/ECTA6158
   Web of Science ®Google Scholar
• Yu, X., Wang, B.-C., & Pang, D. (2018, June). Social optima in mean field LQ control with local disturbance. In IEEE 14th international conference on control and automation (pp. 630–635). IEEE.
   Google Scholar