Data-driven control of complex dynamical systems

The goal of the project is to investigate the connections between a data-driven approach to the direct control design of dynamical systems and the approach to identification and control of nonlinear systems based on Koopman operator theory. If such connections are found, they will be used to extend the current catalogue of direct data-driven control design methods that are being produced for nonlinear systems based on the results. The research will start finding a common ground between the approach and the Koopman operator theory. The second step will consist of narrowing down the scope of the research to the specific class of nonlinear polynomial systems.

As a third step, we will consider general nonlinear systems and aim at designing controllers based on a data-dependent representation of the nonlinear system that uses approximate Koopman eigenfunctions as a basis.

Since our approach does not aim at the optimal identification of Koopman eigenfunctions, but it exploits the knowledge of the vector of observables only at the sampling times, a variant of the design that will be considered is to use samples of eigenfunctions obtainable from experiments initialized at non-recurrent surfaces, which could lead to more accurate control design. Finally, we will test our methods on complex robotic systems.