Home > Research Groups > Junior Research Group DART > Research > The Koopman Operator in Control Engineering

The Koopman Operator in Control Engineering

One focus of the DART research group is the development of a methodology for the application of the Koopman theory to nonlinear mechatronic systems, especially with regard to control and observer design. By the transformation to a linear system description, we hope to reduce the computational effort or simplify the online simulation of the internal model in the controller or observer to such an extent that real-time applications, e.g. in a model-predictive control, become possible for systems where this was previously impossible. In addition, there is an almost completely elaborated system theory for linear dynamic systems and thus a variety of proven design methods of control engineering.

For algorithmic investigations, the generally infinite-dimensional Koopman operator is usually approximated numerically as a matrix, so that an observed nonlinear system behavior can be approximated by a linear, finite-dimensional state description. Therefore, our work will focus on numerical approximation methods such as Dynamic Mode Decomposition (DMD) and Extended DMD.

In the area of the Koopman operator, there are thus three fields of research:

  • Extension of linear system theory to nonlinear dynamical systems using the Koopman operator
  • Design of a control system for a nonlinear mechatronic system using a linearly approximated plant model
  • Adaptability of the linearly approximated plant model with respect to system modifications