Adaptive control with stochastic gradient algorithm: rate of convergence

In this paper, we consider the rate of convergence of the parameter estimation error and the cost function for the stochastic approximation type algorithm. The problem is solve in the case of the minimum-variance stochastic adaptive control. It is proven that stochastic approximation algorithm has the same rate of convergence as the one established for the least-squares algorithm. Comparison of the two algorithms is made under the same conditions related to the process noise and the structure of the system model.