Modelling of robust tracking system under unknown upper bounds on perturbations and measurement noise. Part I: estimation of upper bounds

This paper presents an algorithm for robust synthesis in the ℓ1 setup in tracking problem under incomplete prior information. Nominal model in the form of linear discrete-time single-input single-output system is assumed to be known and the upper bounds on exogenous disturbance, measurement noise and coprime factor perturbations to be unknown to controller designer. Robust synthesis is based on relaxed model validation and treating the associated control criterion as the identification criterion. The first part of the paper presents the method of the relaxed model validation and an algorithm for computing the optimal estimates of upper bounds.