Abstract
Recently, Bellman [2] and Aoki [l] h ave p resented methods for determining upper and lower bounds for the solution of the matrix Riccati equation. Their methods are based on guessing certain matrices and solving associated linear equations. In this paper, a duality relationship for a class of linear regulator problems in optimal control theory is defined. It turns out that the duality relationship, in the context of optimal control, makes quite clear the meaning of Bellman and Aoki’s results. Finally a comment is made regarding improvement of the bounds. As indicated, the interpretations are made in an optimal control context; however, analogous interpretations can be given in the context of optimal linear filtering.
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