Abstract
The paper considers the realization of a specified function on the output of a system linear in control. The control realizing the given function has singularities, which are an obstacle to the realization of the specified function on the entire time interval in the class of admissible controls. An approximation of the given function is constructed on the system output. A control is found such that the output is contained in an arbitrarily small neighborhood of the given function. The conditions for the existence of an approximation are obtained, and an algorithm to construct the approximating control is described.
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