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Shape-Based Nonlinear Model Reduction for 1D Conservation Laws

Denis Nikitin 1 Carlos Canudas de Wit 1 Paolo Frasca 1 
1 NECS-POST - Systèmes Commandés en Réseau
Inria Grenoble - Rhône-Alpes, GIPSA-PAD - GIPSA Pôle Automatique et Diagnostic
Abstract : We present a novel method for model reduction of one-dimensional conservation law to the dynamics of the parameters describing the approximate shape of the solution. Depending on the parametrization, each parameter has a well-defined physical meaning. The obtained ODE system can be used for the estimation and control purposes. The model reduction is performed by minimizing the divergence of flows between the original and reduced systems, and we show that this is equivalent to the minimization of the Wasserstein distance derivative. The method is then tested on the heat equation and on the LWR (Lighthill-Whitham-Richards) model for vehicle traffic.
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Submitted on : Tuesday, September 29, 2020 - 11:30:20 AM
Last modification on : Friday, February 4, 2022 - 3:20:37 AM
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Denis Nikitin, Carlos Canudas de Wit, Paolo Frasca. Shape-Based Nonlinear Model Reduction for 1D Conservation Laws. IFAC WC 2020 - 21st IFAC World Congress, Jul 2020, Berlin (virtual), Germany. pp.1-6, ⟨10.1016/j.ifacol.2020.12.1216⟩. ⟨hal-02952161⟩



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