Koopman-based controller design for nonlinear systems with closed-loop guarantees

Koopman operator theory has emerged as a powerful tool for data-driven analysis and
control of nonlinear dynamical systems, enabling (bi)linear representations of
complex dynamics. Its practical application requires finite-dimensional
approximations, which inevitably introduce model errors. Existing approaches often
neglect these errors, limiting the reliability of Koopman-based control.

This thesis closes this gap by presenting a systematic control framework for
nonlinear systems that connects Koopman theory and data-driven modeling to robust
control design with rigorous closed-loop guarantees. The framework consists of two
main components. First, bilinear surrogate models are derived from data using
Koopman operator theory, providing explicit residual error bounds that account for
finite-data and approximation effects. Second, these surrogate models form the basis
for designing robust state-feedback controllers that explicitly incorporate the
model uncertainties, ensuring desired closed-loop properties of the underlying
nonlinear system.

The framework in this thesis provides a rigorous and systematic foundation for
Koopman-based control, establishing both numerical effectiveness and theoretical
closed-loop guarantees, such as exponential stability and quadratic performance, via
linear matrix inequalities and sum-of-squares relaxations.

• By (author) Robin Strässer