Learning identification of a class of stochastic time-varying systems with colored noise

This paper presents a learning identification method for repetitive systems with time-varying parametric uncertainties. The least squares learning algorithm is derived on the basis of repetitive operations over a pre-specified finite time interval. Sufficient conditions for establishing repetitive consistency of the learning algorithm are given, including the persistent excitation condition and the strictly positive real condition. It is shown that the estimates converge to the time-varying values of the parameters, and the complete estimation can be achieved. The learning identification method is also shown to be applicable to periodically time-varying systems. Numerical simulations are presented to demonstrate the effectiveness of the proposed learning algorithms.