Description
We present the standard balancing theory for nonlinear systems, which is based on an analysis around equilibrium points. Its extension to the contraction framework offers computational advantages, and is presented as well. We provide definitions for controllability and observability functions and their differential versions which can be used for simultaneous diagonalization procedures, providing a measure for importance of the states, as can be shown by the relation to the Hankel operator. 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. The difference between controllability and reachability for the variational system is exploited for computational reasons. 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, differential balanced truncation is doable along state trajectories without solving nonlinear partial differential equations.| Periode | 27-feb.-2023 |
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| Evenementstitel | SIAM Conference on Computational Science and Engineering (CSE23) |
| Evenementstype | Conference |
| Locatie | Amsterdam, NetherlandsToon op kaart |
| Mate van erkenning | International |