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Discretized maximum likelihood estimates for adaptive control of ergodic Markov models
Duncan, Tyrone E. Pasik-Duncan, Bozenna Stettner, L.
Duncan, Tyrone E.
Pasik-Duncan, Bozenna
Stettner, L.
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Abstract
Three distinct controlled ergodic Markov models are considered here. The models are a discrete time controlled Markov process with complete observations, a controlled diffusion process with complete observations, and a discrete time controlled Markov process with partial observations. The partial observations for the third model have the special form of complete observations in a fixed recurrent set and noisy observations in its complement. For each of the models an almost self-optimizing adaptive control is given. These adaptive controls are constructed from a family of estimates that use a finite discretization of the parameter set and a finite family of almost optimal ergodic controls by a randomized certainty equivalence method. A continuity property of the information of a model for one parameter value with respect to another is used to establish this almost optimality property.
Description
This is the published version, also available here: http://dx.doi.org/10.1137/S0363012996298369.
Date
1998-03-01
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Society for Industrial and Applied Mathematics
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Keywords
adaptive control, ergodic control, Markov processes, controlled Markov processes, almost optimal adaptive control
Citation
Duncan, Tyrone E., Pasik-Duncan, B., Stettner, L. "Discretized maximum likelihood estimates for adaptive control of ergodic Markov models." (1998) SIAM J. Control Optim., 36(2), 422–446. (25 pages). http://dx.doi.org/10.1137/S0363012996298369.