Determining system theoretic properties from input-output data

One of the drawbacks of many data-driven control approaches is the lack of guarantees for stability, performance and robustness. Instead of directly learning a controller from data, we therefore suggest learning and analyzing certain system theoretic properties from data in order to leverage this knowledge for controller design. In fact, certain system properties such as the operator gain or passivity properties allow for the direct application of well-known feedback theorems, hence leading to insights to the unknown system and providing guarantees for the closed-loop behavior. Therefore, we aim to develop a broad framework for characterizing such properties of an unknown system solely on the basis of input-output trajectories (i) from storage (offline methods), or (ii) obtained from actively conducting simulations or experiments (online methods). In both scenarios, we aim at approaches that come with provable guarantees for broad classes of system properties. Pivotal questions underlying this investigation are: how can we obtain rigorous mathematical guarantees on the system properties for very broad classes of systems, how can we reduce the number of required input-output data tuples, and how can prior knowledge of the system be incorporated into the respective schemes. This framework, in turn, constitutes a fertile soil for applications in biomechanics and biorobotics, where complex systems and their interactions pose almost insurmountable obstacles for state of the art control theory. This leads us to the last pivotal question: how can we exploit this novel methodology in application fields.