Application of Koopman operator theory to system analysis and control

The Koopman operator theory has experienced an extraordinary revival in the last decade.

This operator allows representing a nonlinear system by a linear infinite dimensional operator. Computational techniques have been proposed based on the Extended Mode Decomposition, and the Koopman operator has been exploited for dynamic system analysis an control.

Recently, we have been interested in the following aspects:

• the computation of the regions of attraction of equilibrium points in hyperbolic systems
• the exploitation of the Koopman operator in predictive control