Linear Matrix Inequality Approaches to Koopman Operator Approximation

Understand

The regression problem associated with finding a matrix approximation of the Koopman operator from data is considered.

• The regression problem is formulated as a convex optimization problem subject to linear matrix inequality (LMI) constraints.
• Doing so allows for additional LMI constraints to be incorporated into the regression problem.
• In particular, asymptotic stability constraints, regularization using matrix norms, and even regularization using system norms can be easily incorporated into the regression problem.