Discrete Time Stochastic Adaptive Control

This paper establishes global convergence of a stochastic adaptive control algorithm for discrete time linear systems. It is shown that, with probability one, the algorithm will ensure the system inputs and outputs are sample mean square bounded and the conditional mean square output tracking error achieves its global minimum possible value for linear feedback control. Thus, asymptotically, the adaptive control algorithm achieves the same performance as could be achieved if the system parameters were known.