Optimal adaptive controller for systems with delay

Stochastic adaptive d ‐step‐ahead optimal control is analyzed in this paper. An adaptive controller using the least squares (LS) algorithm and an input matching technique is proposed to combine the globally convergent estimation character of the adaptive tracking and optimally‐based input specification behavior by using a d ‐step‐ahead quadratic cost function. The identification convergence rate of the parameter estimation is based on the LS algorithm. With adaptive control, the d ‐step‐ahead closed‐loop stochastic system is globally stable and the adaptive controller converges to the d ‐step‐ahead optimal controller. Lastly, the consistency of parameter estimators is analyzed and the convergence rate of parameter estimation is obtained. Copyright © 2004 John Wiley & Sons, Ltd.