Ergodic control of a singularly perturbed markov process in discrete time with general state and compact action spaces

Applied Mathematics and Optimization

Volumn 38, Issue 3, 1998, Pages 261-281

  Bielecki, T R ^a,c   Stettner, L ^b  

^a UNIVERSITY OF ILLINOIS AT CHICAGO   (United States)

^b INSTITUTE OF MATHEMATICS   (Poland)

^c NORTHEASTERN ILLINOIS UNIVERSITY   (United States)

Author keywords

Ergodic control; Invariant measure; Limit control principle; Markov process; Singular perturbation

Indexed keywords

CONTROL; DISCRETE TIME CONTROL SYSTEMS; INVARIANCE; PERTURBATION TECHNIQUES; TRANSIENTS;

ERGODIC CONTROL;

MARKOV PROCESSES;

EID: 0032210293     PISSN: 00954616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002459900091     Document Type: Article

References (18)

1. M. Abbad, T. R. Bielecki, and J. Filar, Algorithms for singularly perturbed limiting average control problems, IEEE Transactions on Automatic Control, vol. 37, 1992, pp. 1421-1425.
2. E. Altman and V. Gaitsgory, Control of a hybrid stochastic system, System and Control Letters, vol. 20, 1993, pp. 307-314.
3. A. Bensoussan, Perturbation Methods in Optimal Control, Wiley, New York, 1988.
4. A. Bensoussan and G.L. Blankenship, Singular perturbations in stochastic control, in Singular Perturbations and Asymptotic Analysis in Control Systems, P. Kokotovic, A. Bensoussan, and G. Blankenship, eds., Springer-Verlag, Berlin, 1986, pp. 171-260.
5. T. R. Bielecki and J. Filar, Singularly perturbed Markov control problem: limiting average cost, Annals of Operations Research, vol. 28, 1991, pp. 153-168.
6. T. R. Bielecki and L. Stettner, On some problems arising in asymptotic analysis of Markov processes with singularly perturbed generators. Stochastic Analysis and Its Applications, vol. 6, 1988, pp. 129-168.
7. T. R. Bielecki and L. Stettner, On ergodic control problems for singularly perturbed Markov processes, Applied Mathematics & Optimization, vol. 20, 1989, pp. 131-161.
8. J.L. Doob, Stochastic Processes, Wiley, New York, 1953.
9. F. Delebecque and J.P. Quadrat, Optimal control of Markov chains admitting strong and weak interactions, Automatica, vol. 17, 1981, pp. 281-296.
10. E.B. Dynkin and A.A. Yushkevich, Controlled Markov Processes, Springer-Verlag, Berlin, 1979.
11. V. Gaitsgory, Control of Systems with Slow and Fast Motions: Averaging and Asymptotic Analysis, Nauka, Moscow, 1991 (in Russian).
12. H.J. Kushner, Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems, Birkhauser, Basel, 1990.
13. W.S. Korolyuk and A.F. Turbin, Semimarkov Processes and Their Applications, Naukova Dumka, Kiev. 1976 (in Russian).
14. W.S. Korolyuk and A.F. Turbin, Mathematical Foundations of Phase Enlargement of Composite Systems, Naukova Dumka, Kiev, 1978 (in Russian).
15. J. Neveu, Bases mathematiques du calcul des probabilites, Masson, Paris, 1964.
16. A. Pervozvansky and V. Gaitsgory, Theory of Suboptimal Decisions, Kluwer, Dordrecht, 1988.
17. L. Stettner, On nearly self-optimizing strategies for a discrete-time uniformly ergodic adaptive model, Applied Mathematics & Optimization, vol. 27, 1993, pp. 161-177.
18. S.P. Sethi and Q. Zhang, Hierarchical Decision Making in Stochatic Manufacturing Systems, Birkhauser, Basel, 1994.