This article is from the Active Noise Control FAQ, by Dr. Chris Ruckman
Adaptive control is a special type of active control. Usually the controller employs some sort of mathematical model of the plant dynamics, and possibly of the actuators and sensors. Unfortunately, the plant can change over time because of changes in temperature or other operating conditions. If the plant changes too much, controller performance suffers because the plant behaves differently from what the controller expects. An adaptive controller is one that monitors the plant and continually or periodically updates its internal model of the plant dynamics.
 
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