Dr. Ulf Jönsson
Laboratory for Information and Decision Systems
Massachusetts Institute of Technology
Cambridge, Massachusetts, USA
A useful idea in systems analysis is to divide the system into a nominal part and a perturbation. Attractive conditions for robust stability and robust performance can then be obtained if the nominal part is suitable for computations. The idea is to use Integral Quadratic Constraints (IQCs) to characterize the perturbation and then solve a convex optimization problem defined in terms of the IQCs.
In the first part of the talk we discuss the basic ideas behind the IQC methodology and the computational problems it gives rise to. For this part of the talk we assume that the nominal system is linear time invariant and that the IQCs are used to characterize unmodeled dynamics, uncertainties, nonlinearities, signals, and other system components.
In the second part of the talk we discuss new research on robustness analysis of periodic trajectories. The IQC methods from the first part of the talk are extended to compute robustness margins of nonlinear systems that exhibit a stable periodic solution due to external periodic forcing. This problem has applications in, for example, control problems where the nominal controller is designed to give good tracking and we want to consider robustness with respect to structured dynamic uncertainty in the system.
Our analysis gives rise to a robustness problem for systems with periodic nominal dynamics. We address this problem with an IQC method that results in an infinite dimensional convex optimization problem. An algorithm based on a frequency theorem for periodic systems by Yakubovich is used to solve the optimization problem.
The second part of the talk is joint work with Alexandre Megretski and Chung-Yao Kao.