One-shot data-driven controller certification

We present a one-shot, purely data-driven, method for controller certification. The method is based on an analysis presented in previous works, where theoretical results have been given showing that certification can be obtained by the estimation of the H_∞-norm of a very specific transfer matrix, but without actually pursuing this approach. Accordingly, we propose a procedure for the estimation of the H_∞-norm directly from closed-loop input–output data, which is based on the Markov parameters. Our procedure requires only a single batch of input–output data collected from the plant, unlike previous data-driven approaches, which may require many data batches collected under different circumstances. We also show that the same approach can be applied when the data are acquired in open loop and that the same formulation allows estimation of the closed-loop performance. Simulation examples illustrate the method's features and show that it is significantly more accurate than other known methods when fed by the same data set. Finally, we provide experimental results in a three-tank liquid processing plant to illustrate the method's practical applicability.