The self-tuning of stochastic adaptive pole placement controllers

Considers the problem of the convergence of adaptive pole placement control for linear stochastic systems. Under the assumption of the controllability of the estimated model, it is found that the adaptive pole placement controller always self-tunes, regardless of external excitation. In addition, the author determines the order of external excitation for parameter consistency. It is shown that for the white noise case the parameter consistency occurs when the order of external excitation is equal to or greater than 2-d, where d is the a priori known lower limit of the plant delay