GENERALIZED MINIMUM-VARIANCE ADAPTIVE-CONTROL AND PARAMETER CONVERGENCE FOR STOCHASTIC-SYSTEMS

Two stochastic adaptive control schemes, the stochastic gradient and m odified least squares, are studied. We consider these for scalar ARMAX systems with general input delays. First, when the algorithms are bas ed on generalized minimum variance control with reference tracking, su fficient conditions for stability and optimality are found. This is do ne using martingale convergence analysis. Secondly, we examine paramet er convergence for each of the algorithms, and establish conditions fo r convergence of the parameter estimates to a random multiple of the t rue parameters.