PhD thesis, Cambridge University Department of Engineering, June 2000

Identification for Control: Deterministic Algorithms and
Error Bounds
Paresh Date

This dissertation deals with frequency domain identification of linear systems in a deterministic set-up. A robustly convergent algorithm for identification of frequency response samples of a linear shift invariant plant is proposed. An explicit bound on the identification error is obtained based on suitable a priori assumptions about the plant and the measurement noise. For a finite measurement duration, this algorithm yields (possibly) noisy point frequency response samples of the plant and a worst case error bound. Given such noisy frequency response samples, two different families of worst case identification algorithms are presented. Each of these algorithms yields a model and a bound on the worst case infinity norm of error between the plant and the model, based on a priori and (in some cases) a posteriori data. One of the families of algorithms is robustly convergent and exhibits a certain optimality for a fixed model order. Both the families of algorithms are shown to be implementable as solutions to certain convex optimisation problems. The ideas and numerical techniques used for implementing these algorithms are further used to propose a method for identification in the nu-gap metric.