A finite converging algorithm of restoring the regression function and its use in adaptive control

The article is concerned with restoration of a linear regression function in the presence of mean square constrained perturbations. An algorithm is proposed which possesses a finite depth memory and solving the problem in a finite number of iterations. The algorithm is proved to converge with conditions less restrictive than those needed for convergence of the method of least squares and other statistical estimation procedures. The algorithm solves the problem of adaptive suboptimal control for a wide range of discrete-time nonlinear systems subjected to mean square constrained or white noise perturbations.