Iteratively learning the ℌ∞-norm of multivariable systems applied to model-error-modeling of a vibration isolation system

The aim of this paper is to develop a new datadriven approach for learning the ℌ_∞ -norm of multivariable systems that can be used for model-error-modeling in robust feedback control. The proposed algorithm only requires iterative experiments on the system. Especially for the multivariable situation that is considered in this paper, these experiments have to be judiciously chosen. The proposed algorithm delivers an estimate of the ℌ_∞-norm of an unknown multivariable system, without the need or explicit construction of a (parametric or non-parametric) model. The results are experimentally demonstrated on model-error-modeling of a multivariable industrial active vibration isolation system. Finally, connections to learning control algorithms are established.