methods and systems for estimating differential or difference equations that can govern a nonlinear , time - varying and parameter - varying dynamic process or system . the methods and systems for estimating the equations may be based upon estimations of observed outputs and , when desired , input data for the equations . the methods and systems can be utilized with any system or process that may be capable of being described with nonlinear , time - varying and parameter - varying difference equations and can used for automated extraction of the difference equations in describing detailed system or method behavior for use in system control , fault detection , state estimation and prediction and adaptation of the same to changes in a system or method .