In this research direction we develop the Koopman operator framework for control of complex nonlinear dynamical systems. In this framework, a nonlinear dynamical system is equivalently represented by an infinite-dimensional linear operator whose spectrum provides information about the properties of the underlying system and whose finite-dimensional truncations allow one to use linear techniques to analyze the nonlinear system.

The principal open problem that we tackle is the use of this framework for control within an optimization-based scheme such as model predictive control (MPC) while guaranteeing end-to-end convexity and fully data-driven design. First works on this topic include linear predictors and optimal construction.

The second principal direction tackled is that of structure exploitation within the Koopman operator framework with the aim of improving the scalability and decreasing the data-requirements of the approach; the first work on this topic is here.