Hybrid risk-sensitive mean-field stochastic differential games with application to molecular biology

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We consider a class of mean-field nonlinear stochastic differential games (resulting from stochastic differential games in a large population regime) with risk-sensitive cost functions and two types of uncertainties: continuous-time disturbances (of Brownian motion type) and event-driven random switching. Under some regularity conditions, we first study the best response of the players to the mean field, and then characterize the (strongly time-consistent Nash) equilibrium solution in terms of backward-forward macroscopic McKean-Vlasov (MV) equations, Fokker-Planck-Kolmogorov (FPK) equations, and Hamilton-Jacobi- Bellman (HJB) equations. We then specialize the solution to linear-quadratic mean-field stochastic differential games, and study in this framework the optimal transport of the GlpF transmembrane channel of Escherichia coli, where glycerol molecules (as players in the game) choose forces to achieve optimal transport through the membrane. Simulation studies show that GlpF improves the glycerol conduction more in a higher periplasmic glycerol concentration, which is consistent with observations made in the biophysics literature.

Original languageEnglish (US)
Title of host publication2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Pages4491-4497
Number of pages7
DOIs
StatePublished - 2011
Event2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 - Orlando, FL, United States
Duration: Dec 12 2011Dec 15 2011

Other

Other2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
CountryUnited States
CityOrlando, FL
Period12/12/1112/15/11

Fingerprint

Stochastic Differential Games
Molecular biology
Molecular Biology
Glycerol
Mean Field
Optimal Transport
McKean-Vlasov Equation
Vlasov equation
Biophysics
Fokker Planck equation
Kolmogorov Equation
Hamilton-Jacobi-Bellman Equation
Quadratic field
Event-driven
Brownian movement
Equilibrium Solution
Fokker-Planck Equation
Regularity Conditions
Nash Equilibrium
Conduction

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

Zhu, Q., Hamidou, T., & Başar, T. (2011). Hybrid risk-sensitive mean-field stochastic differential games with application to molecular biology. In 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 (pp. 4491-4497). [6161035] https://doi.org/10.1109/CDC.2011.6161035

Hybrid risk-sensitive mean-field stochastic differential games with application to molecular biology. / Zhu, Quanyan; Hamidou, Tembine; Başar, Tamer.

2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011. 2011. p. 4491-4497 6161035.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Zhu, Q, Hamidou, T & Başar, T 2011, Hybrid risk-sensitive mean-field stochastic differential games with application to molecular biology. in 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011., 6161035, pp. 4491-4497, 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011, Orlando, FL, United States, 12/12/11. https://doi.org/10.1109/CDC.2011.6161035
Zhu Q, Hamidou T, Başar T. Hybrid risk-sensitive mean-field stochastic differential games with application to molecular biology. In 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011. 2011. p. 4491-4497. 6161035 https://doi.org/10.1109/CDC.2011.6161035
Zhu, Quanyan ; Hamidou, Tembine ; Başar, Tamer. / Hybrid risk-sensitive mean-field stochastic differential games with application to molecular biology. 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011. 2011. pp. 4491-4497
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