Research Interests

My main research interests are centered around non-linear modeling and control, game theory, and networks with applications in intelligent transportation systems.

Stability of Non-Linear Dynamical Flow Networks

Flow networks, i.e., where mass flows along links in a graph and is conserved, usually have non-linear properties due to, e.g., capacity constraints or flow dynamics. For networks with specific dynamic properties, it is possible to show both necessary and sufficient conditions for stability, while for more general dynamics, one can rely on sufficient conditions.

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Feedback-based Traffic Light Control

This research aims to develop feedback control policies for traffic lights. With only information about the number of vehicles queueing up at each junction, the proposed control strategy determines both the cycle length of the upcoming cycle and how large fraction of the cycle each phase should be activated. Our control policy does not require any information about the average arrival rate, how the vehicles propagate through the network or the network topology but it is yet still able to keep the queue lengths bounded whenever any controller can do so. That the controller only needs information about the local queue lengths makes it both scalable and robust.

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Dynamic Routing of Multicommodity Flows

In this work, we study the dynamics when different classes of particles propagate through a shared network. The particles can, for instance, be vehicles, where each class of cars is aiming for one specific destination. The particles propagate along the links (roads) in the network, and at each node (junction) the particles decision about which link to follow next depends on the current congestion level on the outgoing links. Under the assumption that the route choices are congestion avoiding, i.e., if the congestion level increases on one outgoing link, the particle is more likely to choose one of the others outgoing links, we show that the dynamical flow network converges to a unique equilibrium. While it has previously been shown that the flow network is resilient to perturbation for a single commodity flow with these routing policies, we show that the heterogeneity of the dynamic route choice behavior may have a negative impact on the network's resilience.

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