Convergence rate of least-squares identification and adaptive control for stochastic systems†

The strong consistency and the convergence rate of least-squares identification for the multidimensional ARMAX model are established under some decaying excitation conditions which are satisfied if both input and output do not grow too fast and the attenuating excitation technique is applied. The parameter-identification results are applied to adaptive-control systems with a quadratic loss function. The rate of convergence of the loss function to its minimum is also obtained.