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 x_{n} = A_{n}x_{n-1}+B_{n}W_{n} and the output equation y_{n} = C_{n}x_{n}+D_{n}W_{n} relate the finite-dimensional vectors x_{n}, y_{n} and wn. The initial state x0is known to belong to a set X0and each wn. to a set Wn, where X_{0}, W_{1}, . . . , W_{N} are compact and convex. Define S_{n}(y_{1}, ... , y_{n}) as the set of all possible values of xncompatible with observation of outputs y_{1}, ... , y_{n} ; it is compact and convex. Snplays the same role as the a posteriori distribution in the stochastic case and is determined recursively by S_{n-1}(y_{1}, ... , y_{n-1}) and yn. The sets involved are completely characterized by their support functions. The law of evolution of the support function of Snis established. Some special cases and applications are pointed out.
Keywords :
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 :
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