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State Estimation in Freeway Traffic Systems

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Book cover Freeway Traffic Modelling and Control

Part of the book series: Advances in Industrial Control ((AIC))

Abstract

Freeway networks are generally equipped with different types of sensors which are able to measure traffic conditions in real time. Such sensors are placed in fixed positions on the road network and, hence, measure traffic variables in specific positions, often far from each other, because their number is limited by technological and financial issues. In addition, the measurements provided by traffic sensors can be noisy and affected by failures. On the other hand, for designing efficient traffic control and monitoring systems, it is required to know the values of the traffic variables (flow, density, speed) on the different road segments, in real time. For these reasons, the problem of traffic estimation is quite relevant and has attracted the attention of researchers in the past decades. Such a problem will have to face new challenges in the near future, due to the fast development of intelligent and connected vehicles, which are able to measure traffic states and to transmit them in real time. These new technologies will enable much more traffic information than in the past, but providing mobile data that are, by nature, disaggregated and asynchronous.

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Notes

  1. 1.

    An autonomous switched linear system with switching function s(k) expressed as

    $$\begin{aligned}&{\underline{\mathop {x}}}(k+1)=A^{s(k)}{\underline{\mathop {x}}}(k) + B_{\omega }^{s(k)}{\underline{\mathop {\omega }}}(k) \\&{\underline{\mathop {z}}}(k)=C_x^{s(k)}{\underline{\mathop {x}}}(k) + C_{\omega }^{s(k)}{\underline{\mathop {\omega }}}(k) \end{aligned}$$

    is said to have \(\gamma \)-performance if the undisturbed system (i.e. with \({\underline{\mathop {\omega }}}(k)= 0\)) is asymptotically stable and, under zero initial conditions, the following relation is verified

    $$\begin{aligned} \sum _{k=0}^{\infty } {{\underline{\mathop {z}}}^{\text {T}}(k){\underline{\mathop {z}}}(k)} < \gamma ^2 \sum _{k=0}^{\infty } {{\underline{\mathop {\omega }}}^{\text {T}}(k){\underline{\mathop {\omega }}}(k)} \quad \forall {\underline{\mathop {\omega }}}(k)\in \mathscr {L}_2 \end{aligned}$$

    .

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Authors and Affiliations

  1. Department of Electrical, Computer and Biomedical Engineering, University of Pavia, Pavia, Italy

    Antonella Ferrara

  2. Department of Informatics, Bioengineering, Robotics and Systems Engineering, University of Genoa, Genoa, Italy

    Simona Sacone & Silvia Siri

Authors
  1. Antonella Ferrara
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  2. Simona Sacone
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  3. Silvia Siri
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Correspondence to Antonella Ferrara .

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Ferrara, A., Sacone, S., Siri, S. (2018). State Estimation in Freeway Traffic Systems. In: Freeway Traffic Modelling and Control. Advances in Industrial Control. Springer, Cham. https://doi.org/10.1007/978-3-319-75961-6_7

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  • DOI: https://doi.org/10.1007/978-3-319-75961-6_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-75959-3

  • Online ISBN: 978-3-319-75961-6

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