Parameter-tracking models for adaptive control systems

A convenient means of parameter estimation in some systems is to use an automatic parameter-tracking model. The tracking model operates on the input and output signals of the system and automatically determines the unknown parameters. The parameters are adjusted according to a steepest-descent procedure applied to a suitable error function. A systematic method for deriving a variety of possible tracking models is discussed. The tracking models are classified into two types. A type 1 tracking system is stable for all combinations of initial conditions and input signals. If a tracking system is not of-type 1 it is designated as being of type 2. It is shown that a type 2 system behaves like a type 1 system in a linear range. New results dealing with factorisation, model response and model stability are given.