Control of freeway traffic using ramp metering is a "boundary control" problem when modeling is approached using widely adopted coupled hyperbolic PDE models of the Aw-Rascle-Zhang type, which include the velocity and density states, and which incorporate a model of driver reaction time. Unlike the "free traffic" regime, in which ramp metering can affect only the dynamics downstream of the ramp, in the "congested traffic" regime ramp metering can be used to suppress stop-and-go oscillations both downstream and upstream of the ramp - though not both simultaneously. Controlling the traffic upstream of a ramp is harder - and more interesting - because, unlike in free traffic, the control input doesn’t propagate at the speed of the vehicles but at a slower speed, which depends on a weighted difference between the vehicle speed and the traffic density. I will show how PDE backstepping controllers, which have been effective recently in oil drilling and production applications (similarly modeled by coupled hyperbolic PDEs), can help stabilize traffic, even in the absence of distributed measurements of vehicle speed and density, and when driver reaction times are unknown.
Speaker: Miroslav Krstic, UC San Diego
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