Feedback control of nonlinear PDEs using data-efficient reduced order models based on the Koopman operator

Understand

In the development of model predictive controllers for PDE-constrained problems, the use of reduced order models is essential to enable real-time applicability.

• Besides local linearization approaches, Proper Orthogonal Decomposition (POD) has been most widely used in the past in order to derive such models.
• Due to the huge advances concerning both theory as well as the numerical approximation, a very promising alternative based on the Koopman operator has recently emerged.
• In this chapter, we present two control strategies for model predictive control of nonlinear PDEs using data-efficient approximations of the Koopman operator.