Abstract:

Fluid-like models, such as the Lighthill-Whitham-Richards (LWR) model and their discretizations like Daganzo’s Cell Transmission Model (CTM), have proven successful in modeling traffic networks. In general, these models are not linear; they employ discontinuous dynamics or nonlinear terms to describe phenomena like shock waves and phantom jams. Given the complexity of the dynamics, it is not surprising that the stability properties of these models are not yet well characterized. Recent results have shown the existence of a unique equilibrium in the free flow regime for certain classes of networks modeled by the CTM; however, these results restrict inflows to the system to be bounded or constant. Further, it is of interest to understand the system behavior in congested regimes since links in various practical networks are often congested.

In the first part of this talk, we analyze traffic flow on a network modeled by the CTM. We show that the trajectories of the system are persistent in every mode of the system and that if the inflows are constant, the system admits multiple congested equilibria. We then draw upon entropy-like Lyapunov functions used in chemical reaction network theory to show that these equilibria are locally asymptotically stable. With further restrictions on system inflows, these equilibria degenerate to the free flow equilibrium in existing results. In the second part of the work, we focus on mitigating urban traffic congestion. Traditionally, urban traffic congestion control has been carried out via fixed-time or partially real-time traffic light scheduling policies obtained using models that are developed and calibrated offline. With the increasing ubiquity of mobile devices and connected vehicles, it is now possible to obtain real-time traffic density estimates in urban transportation networks. We will develop a scalable compositional control algorithm to mitigate congestion in urban transportation networks that uses real-time local information and local controllers (traffic lights) to limit the propagation of congestion in the network. The algorithm relies on using the traffic data to learn a control-oriented piecewise affine hybrid dynamical fluid model of urban traffic with desirable dynamical properties like monotonicity in certain operating regimes, which is of independent interest.

This work has been done jointly with Sivaranjani Seetharaman, Sadra Sadraddini, and Calin Belta.

Speaker Bio:

Vijay Gupta is in the Elmore Family School of Electrical and Computer Engineering at Purdue University. He received his B. Tech degree at Indian Institute of Technology, Delhi, and his M.S. and Ph.D. at California Institute of Technology, all in Electrical Engineering. He is a fellow of the IEEE and received the 2018 Antonio J Ruberti Award from the IEEE Control Systems Society, the 2013 Donald P. Eckman Award from the American Automatic Control Council and a 2009 National Science Foundation (NSF) CAREER Award. His research and teaching interests are broadly in the interface of communication, control, distributed computation, and human decision making.