Optimization-based design of data-integrated controllers

Modern control theory offers abundant methods for the design of feedback loops that enforce a certain desired behaviour with mathematical guarantees. Remarkably, proofs of stability and performance in many if not all these controller design strategies are based on dissipativity theory as is well-developed for first-principles models of dynamical systems. In view of its trajectory-interpretation, the dissipativity approach offers an ideal setting for handling dynamical systems that are represented by first principles and input-output data, as investigated in PN 4-1. In this project we target at expanding controller synthesis methods to systems that are described by models with data integration and with a specific emphasis on guarantees for robustness of stability and performance. Moreover, in extending the scheduling approach to control, which is so far mostly limited to adaptations in reaction to time-varying parametric changes, new techniques will allow the design of controllers that are capable of adapting structurally to newly incoming online data or even to changes in the dynamics, all equipped with mathematical certificates for the controlled system. First steps will be taken in pursing the longer-term goal to enhance these offline designs with online learning capabilities and with guarantees for the stable operation of the resulting adaptive mechanisms.