Linear Matrix Inequality Approaches to Koopman Operator Approximation
This work provides a new computational framework for approximating the Koopman operator, which is relevant for researchers and practitioners working with dynamical systems and data-driven modeling.
This paper addresses the problem of approximating the Koopman operator from data by formulating the regression as a convex optimization problem with linear matrix inequality (LMI) constraints. This LMI framework allows for the incorporation of additional constraints such as asymptotic stability and various forms of regularization.
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.