Description
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. We show that differential balancing has close relationships with the Fréchet derivative of the nonlinear Hankel operator. Furthermore, we take a generalized balancing approach in order to have a computationally more feasible method. Error bounds for model reduction by generalized balancing are provided.In addition, we propose an empirical balancing method 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. We further develop an approximation method, which only requires trajectories of the original nonlinear system. The method is validated on a nonlinear system of order 100.
This is joint work with Yu Kawano
| Periode | 16-sep.-2021 |
|---|---|
| Evenementstitel | Third IFAC Conference on Modelling, Identification and Control of Nonlinear Systems (MICNON 2021) |
| Evenementstype | Conference |
| Locatie | Tokyo, JapanToon op kaart |