Gramian-Based Optimization for the Analysis and Control of Traffic Networks

Abstract

This paper proposes a simplified version of classical models for urban transportation networks, and studies the problem of controlling intersections with the goal of optimizing network-wide congestion. Differently from traditional approaches to control traffic signaling, a simplified framework allows for a more tractable analysis of the network overall dynamics, and enables the design of critical parameters while considering network-wide measures of efficiency. Motivated by the increasing availability of real-time high-resolution traffic data, we cast an optimization problem that formalizes the goal of minimizing the overall network congestion by optimally controlling the durations of green lights at intersections. Our formulation allows us to relate congestion objectives with the problem of optimizing a metric of controllability of an associated dynamical network. We then provide a technique to efficiently solve the optimization by parallelizing the computation among a group of distributed agents. Lastly, we assess the benefits of the proposed modeling and optimization framework through microscopic simulations on typical traffic commute scenarios for the area of Manhattan. The optimization framework proposed in this study is made available online on a Sumo microscopic simulator based interface [1].

Control of Average and Deviation in Large-Scale Linear Networks

“…2) Control of average and deviation: Find the control law u = u(y,V ) for the system (2) such that lim t→∞ y(t) = y d , and V is minimized. 1 Section III is devoted to the first problem of average control, while Section IV shows the solution for the second problem of simultaneous control of average and deviation.…”

“…It is obvious that f (x)g(x) = 1 − x. Now take n-th derivative of this multiplication: (56) Function g(x) is a polynomial of the degree 2, thus its derivatives can be explicitly written: g (0) (0) = 1, g (1) (0) = −2α, g (2) (0) = 2α, (…”

“…and all higher derivatives are zero. Moreover, (1 − x) (0) (0) = 1 and (1 − x) (1) (0) = −1 with all higher derivatives also zero.…”

“…T HE control of large-scale dynamical networks is a challenging and important question in modern control theory. Its importance originates from its multiple applications to vital systems in technology, nature and society, such as urban traffic networks [1], social networks [2], fleets of robots [3] and power networks [4]. Its difficulty originates from the large dimensionality of these real-world networks, where the number of states can reach millions.…”

Multi-Objective Robust Optimization for the Traffic Sensors Location Problem

“…This relationship is approximated with certain functional forms and the associated uncertainties in approximation errors are handled by using robust optimization techniques. Bianchin and Pasqualetti [47] studied the problem of optimizing the traffic network overall efficiency by controlling the signalized intersections to optimize vehicle evacuation by designing and controlling the durations of green lights at intersections under congestion conditions.…”