Minyi Huang

Professor     FIEEE  

School of Mathematics and Statistics Carleton University  1125 Colonel By Drive  Ottawa, ON  CANADA K1S 5B6  Office: HP 5269 Tel: +1 (613) 520-2600 ext. 8022   Email: mhuang at math dot carleton dot ca

Short Bio    

Research Areas

Mean Field Stochastic Control


A brief overview -- Inspired by ideas from statistical physics, this beautiful area, as a new branch of systems and control theory, is developed by taking an interacting particle approach where the mean field or mass effect serves as the medium for each agent to interact with others in the course of decision making. By studying an infinite population limit, one has the possibility of obtaining simple and useful strategies in a practical large but finite population model. This analytical machinery sheds light on the formation of collective behavior in large complex decision models involving many agents by relating it to the micro-behavior of individuals. When the agents are noncooperative (selfish), this conceptual framework leads to the development of mean field game (MFG) theory. If the agents are cooperative (altruistic), this gives rise to social optimization. The overall methodology provides the ground to develop rich results in stochastic analysis, control theory (including dynamic games), partial differential equations, and numerical analysis. The applications include engineering (communication networks, power systems, etc.), economic theory, finance, among others.

Some links:
wiki [Mean Field Game Theory]
[Mean field games] Introduction by P.E. Caines in Encyclopedia of Systems and Control.
Technical side: The 2011 slides [pdf] at University of Warwick, UK
Ideas: An earlier 2006 research description [pdf] when I was in Melbourne, Australia!
Tao's [MFG Blog], Popular science [MFG tutorial] of L.N. Hoang
A 3-hour Tutorial on Mean Field Games [Part I] [Part II] (Presented at Institute for Mathematical Sciences, National University of Singapore, June 2018)

Control and Games over Large-Scale Networks


Stochastic Algorithms in Multi-Agent Systems (Related slides [pdf])

Editorial/Professional Services

• IEEE Trans Autom Control     IMA J Math Control Info


• Editorial Services for special issues:
  
  • Journal of Systems Science and Complexity: special issue on Recent Advances in Systems and Control (in honor of the 80th Birthday of Professor Peter E. Caines), vol. 38, no. 1, 2025
  • Asian Journal of Control: special issue on Mean Field Games and Mean Field Control, vol. 26, no. 2, 2024

Opportunities for Graduate Studies

If you are interested in my research areas and wish to pursue graduate studies, please contact me by email.

Publications (Google Scholar)

Recent Papers and Talks at Meetings

1. P.E. Caines and M. Huang. "Mean field games on sparse network limits: Laplexion dynamics and epsion-Nash equilibria". Presented at the 64th IEEE CDC, Rio de Janeiro, Brazil, 2025.


2. Y. Wang and M. Huang. "Large-population risk sensitive linear-quadratic optimal control: decentralized feedback". Presented at the 64th IEEE CDC, Rio de Janeiro, Brazil, 2025.


3. X. Yang and M. Huang. "Linear quadratic mean field Stackelberg games: Master equations and time consistent feedback strategies". Presented at the 60th IEEE CDC (virtual), Austin, TX, Dec 2021.


4. M. Huang and S. L. Nguyen. "Linear-quadratic mean field social optimization with a major player". Preprint, July 2018.

Book Chapters

1. M. Huang and Y. Ma. "Binary mean field stochastic games: stationary equilibria and comparative statics", in Modeling, Stochastic Control, Optimization, and Applications, editors G. Yin and Q. Zhang, Springer, pp. 283-313, 2019 [arXiv pdf].


2. P.E. Caines, M. Huang, and R.P. Malhame, "Mean Field Games". In Handbook of Dynamic Game Theory, T. Basar and G. Zaccour Eds., pp. 345-372, Springer, Berlin, 2017 [pdf].


3. M. Nourian, P.E. Caines, R.P. Malhame, and M. Huang. "Leader-follower Cucker-Smale type flocking synthesized via mean field stochastic control theory". In Brain, Body and Machines, (Proceedings of CIM 25th Anniversary Symposium, McGill University), J. Angeles el. al. Eds., pp. 283-298, Springer, Berlin, 2010.


4. M. Huang, P.E. Caines, and R.P. Malhame. "Large population stochastic dynamic games: the Nash certainty equivalence principle and adaptation". In Forever Ljung in System Identification, T. Glad and G. Hendeby Eds., pp. 35-60, Studentlitteratur, Lund, Sweden, 2006.


5. M. Huang, R.P. Malhame and P.E. Caines. "Nash equilibria for large-population linear stochastic systems of weakly coupled agents". In Analysis, Control and Optimization of Complex Dynamic Systems (GERAD 25th Annivesary Series), E. K. Boukas and R. P. Malhame Eds., Chapter 9, pp. 215-252, Springer, New York, 2005. [pdf] (Chapter 9 in book).

Journal Papers

1. T. Chen and M. Huang. Risk-sensitive linear-quadratic-Gaussian graphon mean-field games". Submitted, Aug 2025 (under minor revision). (Also presented at the SIAM Conference on Contorl and Its Appl., July 2025.)


2. M. Huang, S.-J. Sheu, and L.-H. Sun. "Mean field social optimization: feedback person-by-person optimality and the dynamic programming equation". Submitted Aug 2024 (accepted). [long vers].


3. P. E. Caines, M. Huang, R. Foguen-Tchuendom, and S. Gao. "GMFG critical nodes for control affine systems with exponentiated costs". Systems and Control Letters, vol. 206, December 2025, paper 106280 (7 pages).


4. X. Chen, Y. Wu, X. Yi, M. Huang, and L. Shi. "Linear convergent distributed Nash equilibrium seeking with compression". IEEE Trans. Automatic Control, vol. 70, no. 5, p. 3316-3323, 2025.


5. Y. Wang and M. Huang. "Risk-sensitive linear-quadratic mean-field games: asymptotic solvability and decentralized O(1/N)-Nash equilibria". Journal of Systems Science and Complexity. vol. 38, no. 1, p. 436-459, 2025.


6. R. Foguen-Tchuendom, S. Gao, P. E. Caines, and M. Huang. "Infinite horizon LQG graphon mean field games: explicit Nash values and local minima". Systems and Control Letters, vol. 187, May 2024, paper 105780 (9 pages).


7. B. Wang and M. Huang. "Mean field social control for production output adjustment with noisy sticky prices". Dynamic Games and Applications, 2023 https://doi.org/10.1007/s13235- 023-00512-z


8. S. Gao, P. E. Caines, and M. Huang. "LQG graphon mean field games: analysis via graphon invariant subspaces". IEEE Trans. Automatic Control, vol. 68, no. 12, p. 7482-7497, 2023.


9. Z. Xu, T. Shen, and M. Huang. "Model-free policy iteration approach to NCE-based strategy design for linear quadratic Gaussian games". Automatica, vol. 155, Sept. 2023.


10. P.E. Caines, D. Ho, M. Huang, J. Jian, and Q. Song. "Graphon mean field game equations: individual agent affine dynamics and mean field dependent performance functions". ESAIM: Control, Optimisation and Calculus of Variations., vol. 22, 2022. [doi]


11. M. Huang and X. Yang. "Linear quadratic mean field social optimization: asymptotic solvability and decentralized control". Applied Math. Optim., vol. 84, pp. 1969--2010, 2021 [pdf], [arxiv pdf].


12. P.E. Caines and M. Huang. "Graphon mean field games and their equations". SIAM J. Control Optim. vol. 59, no. 6, pp. 4373--4399, 2021 [pdf], [arxiv pdf, long vers].


13. M. Huang and X. Yang. "Linear quadratic mean field games: Decentralized $O(1/N)$-Nash equilibria". Journal of Systems Science and Complexity, vol. 34, no. 5 (special issue in honor of the 60th birthday of Prof. Lei Guo), pp. 2003--2035, 2021 [pdf].


14. M. Huang. "Linear-quadratic mean field games with a major player: Nash certainty equivalence versus master equations". Communications in Information and Systems, vol. 21, no. 3 (special issue in honor of the 80th birthday of Prof. Tyrone Duncan), pp. 441--471, 2021 [pdf], [arxiv pdf].


15. Y. Wu, J. Wu, M. Huang, and L. Shi. "Mean-field transmission power control in dense networks". IEEE Trans. Control of Network Systems, vol. 8, no. 1, pp. 99--110, Mar 2021.


16. M. Huang and M. Zhou. "Linear quadratic mean field games: Asymptotic solvability and relation to the fixed point approach". IEEE Transactions on Automatic Control, vol. 65, no. 4, pp. 1397-1412, Apr 2020 [pdf].


17. Y. Ma and M. Huang. "Linear quadratic mean field games with a major player: The multi-scale approach". Automatica, vol. 113, no. 3, Mar 2020 [pdf, long vers].


18. X. Chen and M. Huang. "Linear-quadratic mean field control: the invariant subspace method". Automatica, vol. 107, pp. 582-586, 2019, available online [here].


19. B. Wang and M. Huang. "Mean field production output control with sticky prices: Nash and social solutions". Automatica, vol. 100, pp. 90-98, 2019 [pdf].


20. J. Huang and M. Huang. "Robust mean field linear-quadratic-Gaussian games with unknown L²-Disturbance". SIAM J. Control Optim., vol. 55, no. 5, pp. 2811-2840, 2017 [pdf].


21. M. Huang and S. L. Nguyen. "Mean field games for stochastic growth with relative utility". Applied Math Optim: special issue in mean field games. vol. 74, pp. 643-668, 2016 [pdf].


22. M. Huang and Y. Ma. "Mean field stochastic games: Monotone costs and threshold policies" (in Chinese). Scientia Sinica Mathematica. vol. 46, no. 10, 1445-1460, 2016 [pdf]. An English version [pdf] updated from the Chinese version but containing the same assumptions and results.


23. A. Al-Zahrani, F.R. Yu, M. Huang. "A joint cross-layer and co-layer interference management scheme in hyper-dense heterogeneous networks using mean-field game theory". IEEE Transactions on Vehicular Technology. vol. 65, no. 3, pp. 1522-1535, 2016.


24. B. Djehiche and M. Huang. "A characterization of sub-game perfect equilibria for SDEs of mean field type". Dynamic Games and Applications, vol. 6, pp. 55-81, 2016 [pdf].


25. M. Huang, T. Li, and J.-F. Zhang. "Stochastic approximation based consensus dynamics over Markovian networks". SIAM Journal on Control and Optimization, vol. 53, no. 6, pp. 3339-3363, 2015 [pdf].


26. Y. Wang, F.R. Yu, H. Tang, and M. Huang. "A mean field game theoretic approach for security enhancements in mobile ad hoc networks". IEEE Trans. Wireless Commun., vol. 13, no. 3, pp. 1616-1627, Mar 2014.


27. M. Huang. "A mean field capital accumulation game with HARA utility". Dynamic Games and Applications: special issue on mean field games, vol. 3, pp. 446-472, 2013 [pdf].


28. M. Nourian, P.E. Caines, R.P. Malhame, and M. Huang. "Nash, social and centralized solutions to consensus problems via mean field control theory". IEEE Transactions on Automatic Control, vol. 58, no. 3, pp. 639-653, Mar. 2013.


29. M. Huang. "Stochastic approximation for consensus: a new approach via ergodic backward products". IEEE Transactions on Automatic Control, vol. 57, no. 12, pp. 2994-3008, Dec. 2012 [pdf].


30. 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 Transactions on Automatic Control, vol. 57, no. 11, pp. 2801-2816, Nov. 2012 [pdf].


31. S.L. Nguyen and M. Huang. "Linear-quadratic-Gaussian mixed games with continuum-parametrized minor players". SIAM J. Control and Optimization, vol. 50, no. 5, pp. 2907-2937, 2012 [pdf].


32. H. Tang, F.R. Yu, M. Huang, and Z. Li. "Distributed consensus-based security mechanisms in cognitive radio mobile ad hoc networks". IET Communications, vol. 6, no. 8, pp. 974-983, 2012.


33. M. Huang, P.E. Caines, and R.P. Malhame. "Social optima in mean field LQG control: centralized and decentralized strategies". IEEE Transactions on Automatic Control, vol. 57, no. 7, pp. 1736-1751, July 2012 [pdf].


34. M. Nourian, R.P. Malhame, M. Huang, and P.E. Caines. "Mean field (NCE) formulation of estimation based leader-follower collective dynamics". International Journal of Robotics and Automation, vol. 26, no. 1, pp. 120-129, 2011.


35. M. Huang, P.E. Caines, and R.P. Malhame. "The NCE (mean field) principle with locality dependent cost interactions". IEEE Transactions on Automatic Control, vol. 55, no. 12, pp. 2799-2805, Dec. 2010 [pdf].


36. M. Huang, S. Dey, G.N. Nair, and J.H. Manton. "Stochastic consensus over noisy networks with Markovian and arbitrary switches". Automatica, vol. 46, no. 10, pp. 1571-1583, Oct. 2010 [pdf].


37. F.R. Yu, M. Huang and H. Tang. "Biologically inspired consensus-based spectrum sensing in mobile Ad Hoc networks with cognitive radios". IEEE Network: Special Issue on BioInspired Communications, pp. 26-30, May/June, 2010 [pdf].


38. M. Huang and J.H. Manton. "Stochastic consensus seeking with noisy and directed inter-agent communication: fixed and randomly varying topologies". IEEE Transactions on Automatic Control, vol. 55, no. 1, pp. 235-241, Jan. 2010 [pdf].


39. M. Huang. "Large-population LQG games involving a major player: the Nash certainty equivalence principle". SIAM Journal on Control and Optimization, vol. 48, no. 5, pp. 3318-3353, 2010 [pdf].


40. Z. Li, F.R. Yu, and M. Huang. "A distributed consensus-based cooperative spectrum sensing scheme in cognitive radios". IEEE Transactions on Vehicular Technology, vol. 59, no. 1, pp. 383-393, Jan. 2010 [pdf].


41. M. Huang and J.H. Manton. "Coordination and consensus of networked agents with noisy measurements: stochastic algorithms and asymptotic behavior". SIAM Journal on Control and Optimization: Special issue on Control and Optimization in Cooperative Networks, vol. 48, no. 1, pp. 134-161, 2009 [pdf].


42. M. Huang, P.E. Caines, and R.P. Malhame. "Large-population cost-coupled LQG problems with non-uniform agents: individual-mass behavior and decentralized epsilon-Nash equilibria". IEEE Transactions on Automatic Control, vol. 52, no. 9, pp. 1560-1571, Sept. 2007 [pdf].


43. M. Huang and S. Dey. "Combined rate and power allocation with link scheduling in wireless data packet relay networks with fading channels". EURASIP Journal on Wireless Communications and Networking, vol. 2007, Article ID 24695, 17 pages, 2007. doi:10.1155/2007/24695 [pdf].


44. M. Huang, P.E. Caines, and R.P. Malhame. "An invariance principle in large population stochastic dynamic games". Journal of Systems Science and Complexity, vol. 20, pp. 162-172, 2007 [pdf].


45. M. Huang and S. Dey. "Dynamic quantization for multisensor estimation over bandlimited fading channels". IEEE Trans. Signal Process., vol. 55, no. 9, pp. 4696-4702, Sept. 2007.


46. M. Huang and S. Dey. "Stability of Kalman filtering with Markovian packet losses". Automatica, vol. 43, pp. 598-607, 2007 [pdf].


47. M. Huang. "Uniqueness of constrained viscosity solutions in hybrid control systems". SIAM Journal on Control and Optimization, vol. 46, no. 1, pp. 332-355, 2007 [pdf].


48. M. Huang, R.P. Malhame, and P.E. Caines. "Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle". Communications in Information and Systems , vol. 6, no. 3, pp. 221-251, 2006 [pdf].


49. M. Huang and S. Dey. "Dynamic quantizer design for hidden Markov state estimation via multiple sensors with fusion center feedback". IEEE Trans. Signal Process., vol. 54, no. 8, pp. 2887-2896, Aug. 2006 [pdf].


50. M. Huang, R.P. Malhame, and P.E. Caines. "Computationally tractable stochastic power control laws in wireless communications". IEEE Trans. Automatic Control, vol. 50, pp. 263-268, Feb. 2005.


51. M. Huang, P.E. Caines, and R.P. Malhame. "Degenerate stochastic control problems with exponential costs and weakly coupled dynamics: viscosity solutions and a maximum principle". SIAM Journal on Control and Optimization, vol. 44, no. 1, pp. 367-387, 2005 [pdf].


52. M. Huang, P.E. Caines, and R.P. Malhame. "Uplink power adjustment in wireless communication systems: a stochastic control analysis". IEEE Trans. Automatic Control, vol. 49, pp. 1693-1708, Oct. 2004 [pdf].


53. M. Huang and L. Guo. "Stabilization of stochastic systems with hidden Markovian jumps", Science in China (Series F), Vol. 44, April 2001, pp. 104-118.


54. F. Xue, L. Guo, and M. Huang. "Towards understanding the capability of adaptation for time-varying systems". Automatica, Vol. 37, 2001, pp. 1551-1560.

Conference Publications     Conference Presentations (no proceedings)

Teaching

• Brightspace, Carleton University