Equilibrium in linear quadratic stochastic games with unknown parameters

ICIC Express Letters

Volumn 3, Issue 2, 2009, Pages 107-113

  Jiménez Lizárraga, Manuel ^a   Basin, Michael ^a   Alcorta Garcia, Ma Aracelia ^a  

^a UNIVERSIDAD AUTÓNOMA DE NUEVO LEÓN   (Mexico)

Author keywords

Nash equilibrium; Stochastic games; Uncertain games

Indexed keywords

LINEAR QUADRATIC; NASH EQUILIBRIUM; SEPARATION PRINCIPLE; STOCHASTIC GAME; STOCHASTIC GAMES; UNCERTAIN GAMES; UNKNOWN PARAMETERS; UNKNOWN STATE;

RANDOM PROCESSES;

GAME THEORY;

EID: 67649516997     PISSN: 1881803X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (17)

1. T. Basar and G. Olsder, Dynamic Noncooperative Game Theory, SIAM, Philadelphia, 1999.
2. M.V.Basin, J.Perez, andM. Skliar, Optimal filtering for partially measured polynomial system states, International J. Adaptive Control and Signal Processing, no.10 1002/acs.1004, 2007
3. M. Basin and M. Skliar, Optimal filtering for partially measured polynomial system states, Proc. of the American Control Conference, pp.4022-4027, 2005.
4. V. Benes, Exact finite dimensional filters for certain diffusions with nonlinear drift, Stochastics, vol.5, pp.65-92, 1981.
5. J. Engwerda, LQ Dynamic Optimization and Differential Games, John Wiley & Sons, West Sussex, England, 2005.
6. M. James and J. Baras, Partially observed differential games, infinite dimensional HJI equation, and nonlinear H control, Technical Research Report, Institute for Systems Research, pp.94-49, 2000.
7. M. Jimenez-Lizarraga and A. Poznyak, Quasi-equilibrium in LQ differential games with bounded uncertain disturbances: Robust and adaptive strategies with pre-identification via sliding mode technique, International Journal of Systems Science, vol.38, no.7, pp.585-599, 2007.
8. G. Kallianpur, Stochastic Filtering Theory, Springer, Berlin, 1980.
9. R. Kalman and R. Busy, New results on linear filtering and prediction theory, ASME Trans., Part D (J. of Basic Engineering), vol.83, pp.95-108, 1961.
10. A. Kian, J. Cruz, and M. Simaan, Stochastic discretetime nash games with constrained state estimators, Journal ofOptimization Theory and Applications, vol.114, no.1, pp.171-188, 2002.
11. H. Kushner, On differential equations satisfied by conditional probability densities of markov processes, SIAM Journal ofControl, no.12, pp.106-119, 1964.
12. R. Liptser and A. Shiryayev, Statistics of Random Processes. Vol I: General Theory, Springer- Verlang, 2000.
13. I. Rhodes and D. Luenberger, Differential games with imperfect state information, IEEE Transactions on Automatic Control, vol.AC-14, no.1, pp.29-38, February 1969.
14. I. Rhodes and D. Luenberger, Stochastic differential games with constrained state estimators, IEEE Transactions on Automatic Control, vol.AC-14, no.5, pp.476-481, October 1969.
15. Y. Sawada, Risk-sensitive tracking control of stochastic systems with preview action, International Journal of Innovative Computing Information and Control, vol.4, no.1, pp.189-198, 2008.
16. W. Wonham, Some applications of stochastic differential equations to nonlinear filtering, SIAM Journal ofControl, vol.2, pp.347-369, 1965.
17. S.-T. Yau, Finite dimensional filters with nonlinear drift. i: A class of filters including both kalman- bucy and benes filters, J. Math. Systems, Estimation and Control, vol.4, pp.181-203, 1994.