We use a Feshbach P-Q partitioning technique to derive a closed one- component integro-differential equation. The resultant equation properly traces the footprint of the target state in quantum control theory. The physical significance of the derived dynamical equation is illustrated by both general analysis and concrete examples. We show that control can be realized by fast-changing external fields, even fast noises. We illustrate the results by quantum memory and controlled adiabatic paths.
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