Iterative correlation-based controller tuning: frequency-domain analysis

The correlation approach is considered for the model-following problem using closed-loop noisy data. The idea is to tune the controller parameters such that the output error between the real closed-loop system and the designed one be uncorrelated with the reference signal. This way, the controller parameters will not be influenced by noise. Since perfect decorrelation is not always possible, the two-norm of the cross-correlation function between the closed-loop output error and an instrumental variable vector is minimized iteratively using the stochastic approximation method. A frequency-domain interpretation of the criterion is given for a simple choice of the instrumental variables. The analysis shows that the noise has asymptotically no effect on the controller parameters. It is shown that the tuned controller compensates for the unmodeled dynamics, so that the designed performances for the initial model are satisfied for the real system as well. The theoretical results are illustrated via a simulation example.