An algorithm for a least-square approximation problem of unknown systems

The authors consider a problem of finding a least-squares approximation parameter that minimizes the output error of unknown systems. When the dimension of the output is equal to the dimension of the input, one can apply the stochastic approximation algorithm. On the other hand, if the dimension of the output is greater than the dimension of the input, one cannot use stochastic approximation. The authors propose an algorithm that is applicable to this problem. This algorithm is an extension of the Robbins-Monro stochastic approximation procedure. A convergence theorem for this proposed procedure is demonstrated.>