Finding

Paper

Abstract

A finite number of decisions, indexed by $\alpha \in A$, are to be taken. Each decision amounts to selecting a point in a measurable space $(U_\alpha ,\mathcal{F}_\alpha )$. Each decision is based on some information fed back from the system and characterized by a subfield $\mathcal{J}_\alpha $ of the product space $(\prod _\alpha U_\alpha ,\prod _\alpha \mathcal{F}_\alpha )$. The decision function for each $\alpha $ can be any function $\gamma _\alpha $ measurable from $\mathcal{J}_\alpha $ to $\mathcal{F}_\alpha $.A property of the $\{ \mathcal{J}_\alpha \} _{\alpha \in A} $ is defined which assures that the setup has a causal interpretation. This property implies that for any combination of choices of the $\gamma _\alpha $, the closed loop equations have a unique solution.The converse implication is false, when card $A > 2$.

Authors

H. Witsenhausen

Journal

Siam Journal on Control

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