Convergence of adaptive control schemes using least-squares estimates

An examination is made of the stability, convergence, asymptotic optimality, and self-tuning properties of stochastic adaptive control schemes based on least-squares estimates of the unknown parameters, when the additive noise is i.i.d. and Gaussian, and the true system is of minimum phase. The author exploits the normal equations of the least-squares method to establish that all stable control law designs used in a certainty-equivalent (i.e. indirect) procedure generally yield a stable adaptive control system. Four results that characterize the limiting behavior precisely are obtained. These general results are specialized to establish the convergence, asymptotic optimality, and self-tuning properties of a variety of proposed adaptive control schemes