Stochastic approximation with two time scales

Systems and Control Letters

Volumn 29, Issue 5, 1997, Pages 291-294

  Borkar, Vivek S ^a  

^a INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

O.d.e. limit; Singular differential equations; Stochastic approximation; Two time scales

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; DIFFERENTIAL EQUATIONS; PERTURBATION TECHNIQUES;

SINGULAR DIFFERENTIAL EQUATION; STOCHASTIC APPROXIMATION; TWO TIME SCALE;

STOCHASTIC CONTROL SYSTEMS;

EID: 0031076413     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-6911(97)90015-3     Document Type: Article

References (12)

1. A. Bensoussan, Perturbation Methods in Optimal Control (Wiley and Gauthier-Villars, New York, Paris, 1988).
2. M.I. Freidlin and A.D. Wentzell, Random Perturbations of Dynamical Systems (Springer, New York, 1984).
3. M. Hirsch, Convergent activation dynamics in continuous time networks, Neural Networks 2 (1987) 331-349.
4. Y.-C. Ho and X.-R. Cao, Perturbation Analysis of Discrete Event Systems (Kluwer, Dordrecht, Boston, 1991).
5. P. Kokotovic, A. Bensoussan and G. Blankenship, eds., Singular Perturbations and Asymptotic Analysis in Control Systems, Lecture Notes in Control and Inform. Sciences, Vol. 90 (Springer, Berlin, 1987).
6. H. Kushner, Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems (Birkhäuser, Boston, 1990).
7. H. Kushner and D. Clark, Stochastic Approximation Methods for Constrained and Unconstrained Systems (Springer, New York, 1978).
8. J. Neveu, Discrete Parameter Martingales (North-Holland, Amsterdam, 1975).
9. G. Papanicolaou, D. Stroock and S.R.S. Varadhan, Martingale approach to some limit theorems, in: M. Reed, ed., Statistical Mechanics, Dynamical Systems and the Duke Turbulence Conference, Duke Uni. Maths. Series, Vol. 3, Durham, NC, 1977.
10. S. Sathiya Keerthi and B. Ravindran, A tutorial survey of reinforcement learning, SADHANA: Indian Academy of Sciences, Proc. in Engineering Sciences, Vol. 19 (1994) 851-889.
11. J. Tsitsiklis, Asynchronous stochastic approximation and Q-learning, Machine Learning 16 (1994) 185-202.
12. T. Yoshizawa, Stability Theory by Liapunov's Second Method (The Mathematical Society of Japan, 1966).