Application of stochastic approximation to on-line system identification

A nonparametric stochastic approximation type of algorithm for on-line identification is considered. By on-line, it is meant that the system is driven by an arbitrary, known input, the control, in addition to an input noise disturbance. Thus, the control effort proceeds in conjunction with identification and is in no way restricted by the requirements of identification. The system is assumed to be all-pole with unknown poles, unknown gain, and noiseless output measurement. Consequently, the procedure is useful when the degree of inaccuracy in the knowledge of the system is much larger than possible output measurement errors. Adaptive control using this procedure is discussed, together with a numerical example.