DocumentCode :
798453
Title :
Sets of possible states of linear systems given perturbed observations
Author :
Witsenhausen, H.S.
Author_Institution :
Bell Telephone Laboratories, Murray Hill, NJ, USA
Volume :
13
Issue :
5
fYear :
1968
fDate :
10/1/1968 12:00:00 AM
Firstpage :
556
Lastpage :
558
Abstract :
The state equation 
and the output equation 
relate the finite-dimensional vectors 
and wn . The initial state x0 is known to belong to a set X0 and each wn . to a set Wn , where 
are compact and convex. Define 
as the set of all possible values of xn compatible with observation of outputs 
; it is compact and convex. Sn plays the same role as the a posteriori distribution in the stochastic case and is determined recursively by 
and yn . The sets involved are completely characterized by their support functions. The law of evolution of the support function of Sn is established. Some special cases and applications are pointed out.
and the output equation relate the finite-dimensional vectors and w are compact and convex. Define as the set of all possible values of x ; it is compact and convex. S and yKeywords :
Linear systems, stochastic; State estimation; Stochastic systems, linear; Cost function; Dynamic programming; Equations; Linear systems; Multidimensional systems; Optimal control; Performance analysis; State-space methods; Trajectory; Writing;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/TAC.1968.1098995
Filename :
1098995
Link To Document :
