Data-driven verification of system theoretic properties for nonlinear systems

During the first funding phase (PN 4-2 “Determining system theoretic properties from input-output data”), we successfully showed that analyzing system theoretic properties, as the operator gain or passivity, from measured trajectories provides valuable insight into the unknown system and allows for a data-driven controller design by the direct application of well-known feedback theorems. However, the suggested approaches are limited to linear systems while many practical applications are nonlinear, and hence more challenging. To address this restriction, we develop within this project a broad framework for determining system properties from measured trajectories with mathematical rigorous guarantees while focusing on general nonlinear systems. One approach is a combination of polynomial approximation and robust control techniques. The system properties that shall be investigated comprise generally dissipativity, IQCs, and incremental properties, due to their special relevance in controller design for unknown plants. Within the framework, we plan to provide offline methods that learn from measured tuples in storage, as well as online schemes where we actively perform simulations or experiments to generate specific data. Pivotal questions underlying this investigation are: (i) how can we obtain rigorous mathematical guarantees on the system properties for very broad classes of systems, (ii) how can we reduce the number of required data samples, (iii) how can prior knowledge of the system be incorporated into the respective schemes. This framework, in turn, constitutes a fertile soil for applications in soft robotics, where complex system behaviour poses almost insurmountable obstacles for model-based control theory.