Linear Matrix Inequality Approaches to Koopman Operator Approximation

2021/02/06 by Steven Dahdah, Dahdah, Steven, James Richard Forbes +1
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Model Reduction and Neural Networks #Numerical methods in engineering #Sparse and Compressive Sensing Techniques #cs.LG #cs.SY #eess.SY #math.DS

paper · pdf · doi:10.48550/arxiv.2102.03613

13 pages

arxiv created 2021/10/18 · arxiv updated 2021/10/20

Abstract

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.

Citations

• Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
• Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control

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