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