Data-enhanced analysis and controller design for uncertain systems

Modern robust control offers computational techniques for analyzing dynamical systems affected by uncertainties and for synthesizing controllers accordingly. These rely on linear fractional representations in which uncertainties are interpreted as dynamical systems with inputs and outputs and on dissipation constraints for describing the behavior of these systems. However, even when employing advanced tools from dissipation theory, the involved uncertainty descriptions mostly do not take experimental data of the underlying system into account. In the first phase of PN 4-3 we tackled this gap from several angles and in tight collaboration with PN 4-1 and PN 4-2. We established novel practical and rigorous frequentist uncertainty bounds for Gaussian processes and embedded these successfully into the robust control framework. This enables the combination with deterministic methods for designing robust controllers with probabilistic guarantees. Moreover, we developed novel robust design techniques for truly mixed models combining prior structural knowledge with data obtained from experiments. They combine a rough uncertainty description with a single noisy input-state trajectory in order to generate a state-feedback controller assuring stability and performance, even on an infinite time horizon. In the second phase of this project, we aim to overcome several still existing restrictions. As a major step forward, we target at employing dynamic supply rates in the dissipation framework. Instead of the currently used rather crude static version for parametric and nonlinear uncertainties. Moreover, we will remove the requirement that measurements of the full system state are available.  Finally, we will investigate how to exploit the so-called scheduled controller design framework for synthesizing data-integrated feedback controllers that learn and adapt themselves to batches of data gathered during the operation of the closed-loop.