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.
Optimal control of systems of conservation laws and application to non-equilibrium traffic steering
Optimale Regelung von Systemen, die Erhaltungsgesetzen unterliegen, und Anwendung auf eine instationäre Verkehrssteuerung
2006
6 Seiten, 2 Bilder, 17 Quellen
Aufsatz (Konferenz)
Englisch
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