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https://www.nist.gov/itl/math/acmd-seminar-optimal-driving-under-traffic-signal-uncertainty

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# ACMD Seminar: Optimal Driving Under Traffic Signal Uncertainty

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Mallory Gaspard*Center for Applied Mathematics, Cornell University*

Tuesday, June 7, 3:00-4:00 EDT (1:00-2:00 MDT)

**A video of this talk is available to NIST staff in the Math channel on NISTube, which is accessible from the NIST internal home page.**

**Abstract:**  Suppose that while driving your car to work, you head toward a steady green traffic light. Although you know that it will turn yellow soon, you don’t know exactly when the change will happen. Under what conditions do you decide to come to a full stop at the intersection to avoid illegally running a red light? On the other hand, under what conditions do you instead decide to speed up and safely clear the intersection while the light is still green or yellow? 

In this talk, we discuss an optimal-control framework for determining a driver’s optimal braking / acceleration behavior in the face of a green traffic light with unknown duration. We interpret this as a control problem where the driver aims to minimize an expected cost based on their fuel use, discomfort from rapid velocity changes, and time to destination. Treating the problem with dynamic programming, we show that the probability distribution on green phase durations gives rise to a sequence of Hamilton-Jacobi-Bellman (HJB) PDEs. We then propose a numerical method to solve the resulting equations and obtain optimal acceleration/braking policy in feedback form. Finally, we present a selection of examples solved with realistic driving parameters which highlight the roles that conflicting optimization objectives and traffic signal uncertainty play in shaping drivers' behavior. 

**Bio:** Mallory Gaspard is a third-year PhD student in the Center for Applied Mathematics at Cornell University. She received her Bachelor’s Degree in Mathematics and Applied Physics from Rensselaer Polytechnic Institute in December 2018. Her primary research interests involve investigating questions of optimality and uncertainty arising in control problems with a variety of applications in areas such as robotics, traffic control, biology, and sociology. In collaboration with her advisor, Alexander Vladimirsky (Cornell University), Mallory aims to incorporate tools from optimal control theory, mathematical modeling, numerical analysis, and computer science in addressing these questions. 

**Host:** Paul Patrone

**Note:**This talk will be recorded to provide access to NIST staff and associates who could not be present to the time of the seminar. The recording will be made available in the Math channel on NISTube, which is accessible only on the NIST internal network. This recording could be released to the public through a Freedom of Information Act (FOIA) request. Do not discuss or visually present any sensitive (CUI/PII/BII) material. Ensure that no inappropriate material or any minors are contained within the background of any recording. (To facilitate this, we request that cameras of attendees are muted except when asking questions.)

Mathematics and statistics

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                -  Paul Patrone  paul.patrone@nist.gov      (301) 975-5551   
                -  Stephen Langer  stephen.langer@nist.gov      (301) 975-5423   
                -  Lochi Orr  lochi.orr@nist.gov      (410) 598-6986   

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