This presentation aims at introducing the basic concepts of the closed loop control of an astronomical AO system. I will start by presenting the temporal behaviour of atmospheric turbulence, and introduce concepts like the Taylor frozen flow hypothesis, Greenwood frequency and coherence time.Other sources of temporal delay introduced by the AO system itself (like delays due to CCD read-out, command computation etc...) will also be shown.
I will then detail how the temporal evolution affects AO control and what control algorithms are being used by closed loop AO systems. I will also show how modal control and other optimization schemes can used to optimize the performance of AO system when faint guide stars are being used.
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