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State observation for heterogeneous quasilinear traffic flow system with disturbances

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Abstract

This paper studies state observation for a heterogeneous quasilinear traffic flow system with disturbances at the inlet of a considered road section. Based on the backstepping method, an observer is designed for the quasilinear traffic flow system with only the boundary measurements at the inlet of the considered road section. The observer is constructed by duplicating the quasilinear system and adding the output injection terms to the partial differential equations and boundary conditions. Making use of the backstepping transformation, the injection gains of the observer system are derived by the computation of kernel equations, which are obtained by mapping the error system into an integral input-to-state stable target system. The applicability of the observer for the design of an output feedback controller stabilizing the quasilinear system is discussed. Finally the assumptions of the design of the observer are numerically checked on a realistic congested traffic scenario.

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Authors and Affiliations

  1. Univ. Grenoble Alpes, Grenoble-INP, Gipsa-lab, CNRS, 38000, Grenoble, France

    Lina Guan & Christophe Prieur

  2. Faculty of Information Technology, Beijing University of Technology, Beijing, China

    Lina Guan & Liguo Zhang

  3. Department of Aerospace Engineering, Universidad de Sevilla, 41092, Sevilla, Spain

    Rafael Vazquez

Authors
  1. Lina Guan
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  2. Christophe Prieur
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  3. Liguo Zhang
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  4. Rafael Vazquez
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Correspondence to Lina Guan.

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The work of L. Guan is supported by a research grant from project PHC CAI YUANPEI under grant number 44029QD, and by MIAI @ Grenoble Alpes (ANR-19-P3IA-0003), and the National Natural Science Foundation of China (NSFC, Grant No. 61873007 and No. 62273014).

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Guan, L., Prieur, C., Zhang, L. et al. State observation for heterogeneous quasilinear traffic flow system with disturbances. Math. Control Signals Syst. (2023). https://doi.org/10.1007/s00498-023-00377-y

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  • DOI: https://doi.org/10.1007/s00498-023-00377-y

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