Abstract: An active system for controlling vibration or sound. The system includes a method for limiting the output gain G from a gradient descent algorithm, such as an LMS algorithm, according to the relationship ##EQU1## and reducing one of first and second filter weights W.sub.1 and W.sub.0 such that G.ltoreq.G.sub.max ensuring the output canceling signal is never saturated. This eliminates the square wave shape which may impart unwanted harmonics or resonances to the dynamic system. In another aspect, the system eliminates drift of the output devices toward saturation when situations are encountered such as singularities in the quadratic performance surface. This is accomplished by applying leakage factor r(k) to a function f(k) at or near a predetermined limit to avoid saturation of the output device. The function f(k) can be the gain G or the weights W(k). Another aspect is to provide a constant, optimum, and stable adaptation rate in an LMS system by providing an optimum adaptation coefficient .mu..sub.