We present a balancing theory for nonlinear systems in the contraction framework. We use prolonged systems to define the controllability and observability functions which can be used for a simultaneous diagonalization procedure, providing a measure for importance of the states. In addition, we propose a data-based model reduction method based on differential balancing for nonlinear systems whose input vector fields are constants by utilizing its variational system. For a fixed state trajectory, it is possible to compute the values of the differential Gramians by using impulse and initial state responses of the variational system. Therefore, balanced truncation is doable along state trajectories without solving nonlinear partial differential equations. The work presented is joint work with Yu Kawano.
Periode
11-sep.-2022
Evenementstitel
pre-MTNS 2022 workshop: Workshop dedicated to the retirement of Arjan van der Schaft