Robust linear system identification in H(infinity).

In modern robust control, control system analysis and design are based on a nominal plant model and (norm) bounds on model uncertainty. The gap between the foundations on which robust control design is built and the tools and results that classical identification theory is able to deliver has fueled a renewed interest in worst-case deterministic formulations of the system identification problem. As a result, system identification techniques should be required to provide guaranteed (deterministic) error bounds in addition to a nominal model. One particular example of a deterministic formulation of an identification problem for robust control is the so-called identification in ${\cal H}\sb\infty.$ In this problem formulation, the experimental data are taken to be the values of the frequency response of the unknown system at a given finite set of frequencies. The identification problem is to map this noisy frequency response data into an identified model. The identification algorithm is required to have many desirable properties. Among them it is required that the worst case identification error (measured in the ${\cal H}\sb\infty$ norm) converge to zero as the noise decreases to zero and the number of frequency response data increases to infinity. Roughly speaking, the term robust convergence refers to this convergence property. In this thesis, the problem of system identification in ${\cal H}\sb\infty$ is investigated in the case when the given frequency response data is not necessarily on a uniformly spaced grid of frequencies. A large class of robustly convergent identification algorithms are derived. A particular algorithm is further examined and explicit worst case error bounds (in the ${\cal H}\sb\infty$ norm) are derived for both discrete-time and continuous-time systems. In the time-domain, the least squares parametric system identification algorithm is analyzed assuming that the noise is a bounded signal. A bound on the worst case parameter estimation error is derived. This bound shows that the worst case parameter estimation error decreases to zero as the bound on the noise is decreased to zero.PhDApplied SciencesMechanical engineeringSystems scienceUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/128965/2/9308261.pd