A recursive self-tuning control scheme for finite Markov chains is proposed wherein the unknown parameter is estimated by a stochastic approximation scheme for maximizing the log-likelihood function and the control is obtained via a relative value iteration algorithm. The analysis uses the asymptotic o.d.e.s associated with these.
Department of Computer Science and Automation, Indian Institute of Science, Bangalore-560012, India
Bibliografia
[1] D. Bertsekas, Dynamic Programming--Deterministic and Stochastic Models, Prentice-Hall, Englewood Cliffs, N.J., 1987.
[2] V. S. Borkar, Identification and adaptive control of Markov chains, Ph.D. Thesis, Dept. of Electrical Engrg. and Computer Science, Univ. of California, Berkeley, 1980.
[3] V. S. Borkar, Topics in Controlled Markov Chains, Pitman Res. Notes in Math. 240, Longman Scientific and Technical, Harlow, 1991.
[4] V. S. Borkar, The Kumar-Becker-Lin scheme revisited, J. Optim. Theory Appl. 66 (1990), 289-309.
[5] V. S. Borkar, On Milito-Cruz adaptive control scheme for Markov chains, ibid. 77 (1993), 385-393.
[6] V. S. Borkar and K. Soumyanath, A new analog parallel scheme for fixed point computation I--theory, submitted.
[7] V. S. Borkar and P. P. Varaiya, Adaptive control of Markov chains I: finite parameter case, IEEE Trans. Automat. Control AC-24 (1979), 953-957.
[8] V. S. Borkar and P. P. Varaiya, Identification and adaptive control of Markov chains, SIAM J. Control Optim. 20 (1982), 470-488.
[9] Y.-S. Chow and H. Teicher, Probability Theory: Independence, Interchangeability, Martingales, Springer, New York, 1979.
[10] B. Doshi and S. Shreve, Randomized self-tuning control of Markov chains, J. Appl. Probab. 17 (1980), 726-734.
[11] Y. El Fattah, Recursive algorithms for adaptive control of finite Markov chains, IEEE Trans. Systems Man Cybernet. SMC-11 (1981), 135-144.
[12] --, Gradient approach for recursive estimation and control in finite Markov chains, Adv. Appl. Probab. 13 (1981), 778-803.
[13] M. Hirsch, Convergent activation dynamics in continuous time networks, Neural Networks 2 (1987), 331-349.
[14] A. Jalali and M. Ferguson, Adaptive control of Markov chains with local updates, Systems Control Lett. 14 (1990), 209-218.
[15] P. R. Kumar and A. Becker, A new family of adaptive optimal controllers for Markov chains, IEEE Trans. Automat. Control AC-27 (1982), 137-142.
[16] P. R. Kumar and W. Lin, Optimal adaptive controllers for Markov chains, ibid., 756-774.
[17] H. Kushner and D. Clark, Stochastic Approximation for Constrained and Unconstrained Systems, Springer, Berlin, 1978.
[18] P. Mandl, Estimation and control in Markov chains, Adv. Appl. Probab. 6 (1974), 40-60.
[19] R. Milito and J. B. Cruz Jr., An optimization oriented approach to adaptive control of Markov chains, IEEE Trans. Automat. Control AC-32 (1987), 754-762.
[20] J. Neveu, Discrete-Parameter Martingales, North-Holland, Amsterdam, 1975.
[21] B. Sagalovsky, Adaptive control and parameter estimation in Markov chains: a linear case, IEEE Trans. Automat. Control AC-27 (1982), 414-417.
[22] Ł. Stettner, On nearly self-optimizing strategies for a discrete-time uniformly ergodic adaptive model, Appl. Math. Optim. 27 (1993), 161-177.
[23] T. Yoshizawa, Stability Theory by Liapunov's Second Method, The Mathematical Society of Japan, 1966.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-zmv24i2p169bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.