Efficient analysis and synthesis tools for robust and scheduled controller design against time-varying and dynamic uncertainties

Project members: S. Dietz, C.W. Scherer

In recent years optimization based robust controller analysis and synthesis techniques have emerged as powerful tools in numerous practical control applications. In particular the development of fast optimization algorithms for solving semi-definite programming problems during the last decade has caused a paradigm shift in control to handle design problems that are deemed untractable with established analytical techniques. Despite impressive progress, it is only partially understood how to effectively incorporate mixtures of dynamic time-invariant and rate-bounded time-varying uncertainties into systematic controller analysis and synthesis algorithms by employing suitable relaxation schemes, and it is largely unexplored how to estimate relaxation errors.

This project aims at developing an integrated theoretical framework for handling uncertainty mixtures by merging time- and frequency-domain descriptions of their properties. Emphasis will be put on the development of structure exploiting numerical algorithms that allow a gradual reduction of relaxation errors and that generate bounds on the involved conservatism. This fundamentally novel strategy leads to the second goal, the development of the corresponding robust and scheduled controller synthesis techniques, with the demonstration of their applicability for regulating systems whose dynamics vary with time or nonlinearly. These schemes will involve a partition of uncertainty value sets such that robust or scheduled controller design will be intimately related to the design of multi-objective and switched controllers for a large number of models. The third goal is to arrive at a fundamentally new understanding of the interrelations of these topics with the design of structured controllers for system network interconnections.