Software sensors design for a class of non linear coupled PDE systems: The Vlasov–Poisson dynamical system

Abstract

This paper presents the synthesis of a state observer for the 1D×1D Vlasov–Poisson (VP) equations. To derive the LPV (linear parameter-varying) formulation of the system, the Vlasov equation is approximated using the discontinuous Galerkin method and the Poisson problem is approximated using the Raviart–Thomas mixed finite element approach. The paper demonstrates the asymptotic and exponential stability of the discretized VP system. Furthermore, the synthesis is extended to include H∞ state estimation. A simulation code has been developed to validate the obtained results.