Extensions of innovations dual control

Extension of the innovations dual control proposed by Milito et al. (1982) to a model with stochastic coefficients containing white noise components is considered first. In the process of extension, the relationship between innovations dual control and the active adaptive control of Goodwin and Payne (1977) is clarified. A drawback of the extended algorithm is pointed out and a modified algorithm is proposed. Secondly, innovations dual control and the modified algorithm are extended to a model with d-step input delays. It is shown that the extensions can be achieved by using optimal predictors of the output up to d − 1 steps ahead, but some approximations are required except for the innovations dual control for d = 2. Simulation results are presented to illustrate that the drawback of extended innovations dual control can be remedied by the proposed modification.