Abstract
An examination is made of linear regulator problems with an additional cost for applying a nonzero control at each instant. The dual of this problem is the least-squares filtering problem with a cost for taking measurements. Because a solution to the general problem involves solving a two point boundary value problem in nonlinear matrix differential or defference equations, two easily-computed suboptimal control schemes and some useful bounds are proposed. A class of problems is also delineated for which the optimum solution has some special properties which enable it to be computed simply and directly.
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