Optimal control is an appealing framework for traffic control problems as the main objective is to maximize the infrastructure usage. A classical approach in optimal control of linear partial differential equations uses adjoint calculus to characterize the necessary conditions of optimality. For nonlinear problems, the same approach can be used iteratively on the linearized dynamics. Nevertheless, it is not clear for conservation laws if the dynamics can be linearized given the irregularity of the fields they generate. An optimal control algorithm is proposed for scalar conservation laws based on the weak formulation and considering the piecewise-C1 structure of the solution. The Roe average method is proposed with an upwind scheme as it captures accurately discontinuities and is devoid of oscillating behaviour. A traffic application is presented that computes the ramp metering rates given the initial and boundary conditions only.


    Access

    Access via TIB

    Check availability in my library


    Export, share and cite



    Title :

    Optimal control of systems of conservation laws and application to non-equilibrium traffic steering


    Additional title:

    Optimale Regelung von Systemen, die Erhaltungsgesetzen unterliegen, und Anwendung auf eine instationäre Verkehrssteuerung




    Publication date :

    2006


    Size :

    6 Seiten, 2 Bilder, 17 Quellen


    Type of media :

    Conference paper


    Type of material :

    Print


    Language :

    English





    Optimal Steering Laws for Variable Speed Control Moment Gyros

    Lee, Hyunjae / Lee, Il-Hyoung / Bang, Hyochoong | AIAA | 2005


    Conservation Versus Balance Laws in Traffic Flow

    Bagnerini, P. / Colombo, R.M. / Corli, A. et al. | British Library Conference Proceedings | 2005


    Modeling and Managing Traffic Flow Through Hyperbolic Conservation Laws

    Colombo, R.M. | British Library Conference Proceedings | 2005


    Some simple CMG steering laws for spacecraft attitude control systems

    Colburn, B.K. / White, L.Yr. / Boland, J.S. | Tema Archive | 1976