We report on recent work [16] on the reachability analysis of nonlinear ordinary differential equations (odes). Relying on Carleman linearization and Krylov projection, we describe a method that, given a nonlinear ode system, generates a small linear approximation of the original dynamics. The construction is independent of the initial condition. Used in conjunction with zonotopes, this yields CKR, an accurate reachability analysis algorithm.
Linearization and Model Reduction in Zonotope-Based Reachability Analysis of Nonlinear ODEs / Boreale M.; Collodi L.. - ELETTRONICO. - 4039:(2025), pp. 140-146.
Linearization and Model Reduction in Zonotope-Based Reachability Analysis of Nonlinear ODEs
Boreale M.
;Collodi L.
2025
Abstract
We report on recent work [16] on the reachability analysis of nonlinear ordinary differential equations (odes). Relying on Carleman linearization and Krylov projection, we describe a method that, given a nonlinear ode system, generates a small linear approximation of the original dynamics. The construction is independent of the initial condition. Used in conjunction with zonotopes, this yields CKR, an accurate reachability analysis algorithm.
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