System identification for robust control
Antoulas, Athanasios C.
Master of Science
In the design of a robust control system, one needs a nominal model together with a quantitative bound on the uncertainty that results from under-modeling and disturbances. In this thesis we do not intentionally seek a nominal model and a quantitative bound, instead, the uncertainty is directly parameterized so that the resulting uncertain model family can be characterized by means of a real parameter vector with at most unit length. This is an innovative approach to the control-oriented system identification, since it is not in accordance with the general philosophy of robust identification. However, it is applicable to the robust synthesis problem by taking advantage of a convex parameterization of robust controllers that simultaneously stabilize the uncertain models in the family. The robust performance problem becomes tractable since it can be converted into a quasi-convex optimization problem with Linear Matrix Inequality (LMI) constraints. The relation between the optimal robust performance and the uncertainty is studied by analyzing the explicit bounds of the maximal robust margin. Model (in)validation is a complement to system identification. In our approach it is an integral ingredient of the process of obtaining robust control-oriented system models. A single model is not invalidated if it is inside the ellipsoid, and thus the intersection of the ellipsoids is not invalidated. In order to make the unfalsified model set (the intersection) fit in our framework, we can compute an optimal ellipsoid bounding the intersection of the ellipsoids. (Abstract shortened by UMI.)
Mathematics; Electronics; Electrical engineering; System science