Mathematics Colloquium

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Stabilization of Coupled Hyperbolic PDE: Calming “Stop-and-Go” Traffic with Backstepping

Speaker: Miroslav Krstic, UCSD

Location: Warren Weaver Hall 1302

Date: Monday, April 22, 2019, 3:45 p.m.

Synopsis:

“Stop-and-go” traffic oscillations require multiple hyperbolic PDEs to capture correctly – as a minimum, separate density and velocity dynamics need to be included, as in the state-of-the-art Aw-Rascle-Zhang model which, unlike the previous `gas dynamics’  imitations of traffic, also includes elements of human behavior (“forward-oriented” attention, collision avoidance, etc.). Instability of the stop-and-go kind arises due to the coupling in the PDEs throughout their domain. While in the far future, with fully automated freeways, control will be possible at each vehicle, allowing the PDEs to be decoupled by feedback, the means of traffic actuation of today are located only at “boundaries,” as in the case of ramp metering at the freeway entrance. Simple collocated static feedback laws do not suffice for stabilizing PDEs that are coupled domain-wide. The domain-wide decoupling with boundary control is possible, however, using the backstepping approach, which also allows estimation of both the states and the unknown parameters of the  freeway and the drivers on it, all from sensing only at the ramp. I will illustrate the theoretical/mathematical and methodological ideas for the boundary control of coupled hyperbolic PDEs within the setting of traffic control and other applications.