Discrete-time entropy formulation of optimal and adaptive control problems

Author

Tsai, Yweting A. ; Casiello, Francisco A. ; Loparo, Kenneth A.

Author_Institution

Dept. of Syst. Eng., Case Western Reserve Univ., Cleveland, OH, USA

Volume

37

Issue

7

fYear

1992

fDate

7/1/1992 12:00:00 AM

Firstpage

1083

Lastpage

1088

Abstract

The discrete-time version of the entropy formulation of optimal control of problems developed by G.N. Saridis (1988) is discussed. Given a dynamical system, the uncertainty in the selection of the control is characterized by the probability distribution (density) function which maximizes the total entropy. The equivalence between the optimal control problem and the optimal entropy problem is established, and the total entropy is decomposed into a term associated with the certainty equivalent control law, the entropy of estimation, and the so-called equivocation of the active transmission of information from the controller to the estimator. This provides a useful framework for studying the certainty equivalent and adaptive control laws

Keywords

adaptive control; entropy; optimal control; adaptive control; certainty equivalent control law; discrete-time entropy; dynamical system; entropy of estimation; optimal control; optimal entropy problem; probability distribution function; total entropy; uncertainty; Adaptive control; Entropy; Equations; Feedback; Frequency; Gaussian processes; Interpolation; MIMO; Optimal control; Transfer functions;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.148379

Filename

148379