Abstract
In this note, we consider the adaptive control of a linear diffusion process with regard to the discounted cost criterion. We show that the certainty-equivalence type of control, analogous to the one considered by Duncan and Pasik-Duncan (Ref. 1), is asymptotically discount optimal in the sense of Schäl (Ref. 2).
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References
Duncan, T. E., andPasik-Duncan, B.,Adaptive Control of Continuous-Time Linear Stochastic Systems, Mathematics for Control, Signals, and Systems, Vol. 3, pp. 45–60, 1990.
Schäl, M.,Estimation and Control in Discounted Stochastic Dynamic Programming, Stochastics, Vol. 20, pp. 51–71, 1987.
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Duncan, T. E., Goldys, B., andPasik-Duncan, B.,Adaptive Control of Linear Stochastic Evolution Systems, Preprint, Department of Mathematics, University of Kansas.
Lipster, R. S., andShiryaev, A. N.,Statistics of Random Processes, I, Springer-Verlag, New York, New York, 1978.
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Communicated by P. Varaiya
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Bielecki, T.R. Adaptive control of continuous-time linear stochastic systems with discounted cost criterion. J Optim Theory Appl 68, 379–383 (1991). https://doi.org/10.1007/BF00941575
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DOI: https://doi.org/10.1007/BF00941575