We present a scheme to realize the arbitrary control of the time evolution of an atom-cavity system via atomic feedback for the generation of an aribitrary quantum state. The scheme contains a Ramsey zone, a high-Q cavity and a two-level Rydberg atom. The atom is injected into the Ramsey zone and the cavity successively. After the passage through the cavity, the atomis sent back and injected into the Ramsey zone and the cavity again, instead of being detected. In this way, we repeat the procedure and realize the arbitrary control of thetime evolution of an atom-cavity system by controlling the interacting time through the atomic velocity.
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