Researchers: Ulf Jönsson, in cooperation with Alexandre Megretski (M.I.T) Chung-Yao Kao (M.I.T).
Sponsor: The Swedish Research Council for Engineering Sciences (TFR).
Applications for periodic system theory abound in science and engineering. Periodic phenomena can appear due to limit-cycle oscillation, forced vibration, or parametric excitation of the system. In this project we consider the questions of robustness and stability for periodic systems. As an example, we are interested in deciding whether periodic solutions remain and if they stay stable when the dynamics of the system changes. In other words, we develop tools for studying robustness against period changing bifurcations.
The results so far are along two different directions. In [C24],[C31], and [R10] we discuss robustness of periodic solutions of non-autonomous systems with respect to structured uncertainty. We use a worst case sensitivity derivatives of the trajectory with respect to the structured uncertainty in order to derive conditions for existence of an exponentially stable periodic solution in a given neighborhood of the nominal solution. In order to solve this problem we need tools for robustness analysis of linear time periodic systems, which is the second direction of research. For this we have shown how integral quadratic constraints and a special convex optimization algorithm can be used for general stability and performance analysis of periodic systems [A17],[C23].
Research 1999/2000
Optimization of power systems under uncertainty
Process modeling, operator training simulation and optimization applied to paper board manufacturing