NDLI: On a Stochastic Optimality of the Feedback Control in the LQG-Problem

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Kabanov, Yu. M. Belkina, T. A. Presman, E. L.
Copyright Year	2004
Abstract	We show that the optimal feedback control $\widehat u$ in the standard nonhomogeneous LQG-problem with infinite horizon has the following property. There is a constant $b_$ such that, whatever $b> b_$ is, the deficiency process of optimal control with respect to any possible control u, i.e., the difference $J_T(\widehat u\hspace{0.2pt})- J_T(u)$ between the optimal cost process $J_T(\widehat u\hspace{0.2pt})$ and the cost process corresponding to control u, is majorated at infinity by a deterministic function $b\log T$. In other words, $b\log T$ is an upper function for any deficiency process. This result, combined with an example of an LQG-regulator where, for certain $b>0$, the function $b\log T$ is not an upper function for certain deficiency processes, gives an answer to the long-standing open problem about the best possible rate function for sensitive probabilistic criteria. Our setting covers the optimal tracking problem.
Starting Page	592
Ending Page	603
Page Count	12
File Format	PDF
ISSN	0040585X
DOI	10.1137/S0040585X97980695
e-ISSN	10957219
Journal	Theory of Probability & Its Applications (TPRBAU)
Issue Number	4
Volume Number	48
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-25
Access Restriction	Subscribed
Subject Keyword	upper functions linear-quadratic regulator controllability optimality almost surely Riccati equation observability Ornstein--Uhlenbeck process martingale law of large numbers
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty

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