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Observers of Vlasov-Poisson system

Abstract : This work focuses on observer's for one-dimensional (1D) Vlasov-Poisson (VP) system. Thanks to the discontinuous Galerkin method (DGM) to put the system into a suitable and explicit state space representation form. Then we construct a state observer of finite dimension that assures asymptotic convergence under weak conditions. Indeed, we introduce a useful Linear Parameter Varying System formulation to compute the observer gain matrix from a Linear Matrix Inequality. Moreover, since matrices obtained by the DGM are tridiagonal, we show that only a reduced order observer is necessary to estimate the whole state of the system. In the noise context, extension to H 8 state estimation is also established.
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https://hal.univ-lorraine.fr/hal-03208653
Contributor : Amadou Cisse <>
Submitted on : Monday, April 26, 2021 - 5:03:11 PM
Last modification on : Wednesday, May 5, 2021 - 3:02:00 AM

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Amadou Cisse, Mohamed Boutayeb. Observers of Vlasov-Poisson system. 21st IFAC World Congress, IFAC 2020, Jul 2020, Berlin, Germany. ⟨10.1016/j.ifacol.2020.12.1647⟩. ⟨hal-03208653⟩

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