Noniterative Data-driven Controller Tuning Using the Correlation Approach

Data-driven controller tuning for model reference control problem is investigated. A new controller tuning scheme for linear time-invariant single- input single-output systems is proposed. The method, which is based on the correlation approach, uses a single set of input/output data from open-loop or closed-loop operation. A specific choice of instrumental variables makes the correlation criterion an approximation of the model reference control criterion. The controller parameters and the correlation criterion are asymptotically not affected by noise. In addition, based on the small gain theorem, a sufficient condition for the stability of the closed-loop system is given in terms of the infinity norm of a transfer function. An unbiased estimate of this infinity norm can be obtained as the solution to a convex optimization problem using an infinite number of noise-free data. It is also shown that, for noisy data, the use of the correlation approach can improve significantly the estimate. The effectiveness of the proposed method is illustrated via a simulation example.