Identification for control: L2 and L∞ methods

Identification of restricted-complexity models for linear time-invariant systems is considered. A method, with ties to model reduction and the extended instrumental variable method, is presented, which uses a cost function based on cross-correlations between the prediction error and some auxiliary variable, such as the input. In open loop and under linear feedback, this method is able to asymptotically approximate the underlying system in L₂ or L_∞ norm without an explicit noise model under noisy conditions. Arbitrary frequency weighting, also depending on the true frequency function, can be used. The method is applied to the identification of models that are suited for control design. It is shown that some model-free methods can be fit into this framework. It is also pointed out that closed-loop stability is not taken into account in the bias tuning due to the fact that L-norms are used