Identification of distributed parameter systems by stochastic approximation

Stochastic approximation schemes are applied to the identification of linear distributed parameter systems. The dependent function is assumed piecewise continuous and is approximated by a finite number of functions chosen from a "complete" system of orthonormal functions. It is also assumed that noisy measurements of the function are available at random points in space and time. Therefore, the identification is performed off-line. The constant parameters multiplying the approximating functions are obtained sequentially by stochastic approximation algorithms that minimize a mean-square error performance criterion.