ITS Berkeley

A Traffic Model for Velocity Data Assimilation

Work, Daniel B.
Blandin, Sébastien
Tossavainen, Olli‐Pekka
Piccoli, Benedetto
Bayen, Alexandre M.
2010

This article is motivated by the practical problem of highway traffic estimation using velocity measurements from GPS enabled mobile devices such as cell phones. In order to simplify the estimation procedure, a velocity model for highway traffic is constructed, which results in a dynamical system in which the observation operator is linear. This article presents a new scalar hyperbolic partial differential equation (PDE) model for traffic velocity evolution on highways, based on the seminal Lighthill-Whitham-Richards (LWR) PDE for density. Equivalence of the solution of the new velocity...

Stealthy Deception Attacks on Water SCADA Systems

Amin, Saurabh
Litrico, Xavier
Sastry, S. Shankar
Bayen, Alexandre M.
2010

This article investigates the vulnerabilities of Supervisory Control and Data Acquisition (SCADA) systems which monitor and control the modern day irrigation canal systems. This type of monitoring and control infrastructure is also common for many other water distribution systems. We present a linearized shallow water partial differential equation (PDE) system that can model water flow in a network of canal pools which are equipped with lateral offtakes for water withdrawal and are connected by automated gates. The knowledge of the system dynamics enables us to develop a deception attack...

Lax–Hopf Based Incorporation of Internal Boundary Conditions Into Hamilton–Jacobi Equation. Part I: Theory

Claudel, Christian G.
Bayen, Alexandre M.
2010

This article proposes a new approach for computing a semi-explicit form of the solution to a class of Hamilton-Jacobi (HJ) partial differential equations (PDEs), using control techniques based on viability theory. We characterize the epigraph of the value function solving the HJ PDE as a capture basin of a target through an auxiliary dynamical system, called ¿characteristic system¿. The properties of capture basins enable us to define components as building blocks of the solution to the HJ PDE in the Barron/Jensen-Frankowska sense. These components can encode initial conditions, boundary...

Incorporation of Lagrangian Measurements in Freeway Traffic State Estimation

Herrera, Juan C.
Bayen, Alexandre M.
2010

Cell-phones equipped with a global positioning system (GPS) provide new opportunities for location-based services and traffic estimation. When traveling on-board vehicles, these phones can be used to accurately provide position and velocity of the vehicle as probe traffic sensors. This article presents a new technique to incorporate mobile probe measurements into highway traffic flow models, and compares it to a Kalman filtering approach. These two techniques are both used to reconstruct traffic density. The first technique modifies the Lighthill–Whitham–Richards partial differential...

Linear and Quadratic Programming Formulations of Data Assimilation or Data Reconciliation Problems for a Class of Hamilton-Jacobi Equations

Claudel, Christian G.
Bayen, Alexandre M.
2010

This article proposes a new method for data assimilation and data reconciliation applicable to systems modeled by conservation laws. The state of the system is written in the form of a scalar Hamilton-Jacobi (HJ) partial differential equation (PDE), for which the solution is fully characterized by a LaxHopf formula. Using the properties of the solution, we prove that when the data of the problem is prescribed in piecewise affine form, the constraints of the model are in standard convex form, and can be computed explicitly. This property enables us to identify a class of data assimilation...

Boundary Stabilization of the Inviscid Burgers Equation Using a Lyapunov Method

Blandin, Sébastien
Litrico, Xavier
Bayen, Alexandre
2010

We consider the problem of stabilization of the inviscid Burgers partial differential equation (PDE) using boundary actuation. We propose a solution to the problem using a Lyapunov approach and prove that the inviscid Burgers equation is stabilizable around a constant uniform state under an appropriate boundary control. We conduct this study in the space of weak solutions of the PDE. Because of the absence of viscosity term, discontinuities can appear in finite time for general initial conditions. In order to handle this feature of the solutions, we decompose the Lyapunov function into a...

Optimal Network Topology Design in Multi-Agent Systems for Efficient Average Consensus

Rafiee, Mohammad
Bayen, Alexandre M.
2010

The problem considered in the present article is optimal design of network topologies in multi-agent systems in order to make communication on the network as efficient as possible for the continuous-time average-consensus protocol. The network design problem can be posed in two different ways. (1) Assuming that the maximum communication cost, i.e. the maximum number of communication links, is known, the goal is to find the network topology which results in the fastest convergence to the consensus (in presence of communication time delays on the links). (2) If a minimum performance of the...

Mobile Millenium Stockholm

Allström, Andreas
Archer, Jeffery
Bayen, Alexandre M.
Blandin, Sébastien
2011

The need for accurate real time traffic information is growing in almost all big cities around the world. One of these cities is Stockholm, recently named as the fifth most congested city in Western Europe. The Mobile Millennium Stockholm project was initiated by the Swedish Transport Administration in order to address the need for a useful and timely traffic information system. The purpose of the project is to assimilate the knowledge gained from the Mobile Millennium project at University of California, Berkeley and develop new methods for data fusion, one of the most challenging...

Viability Theory: New Directions

Aubin, Jean-Pierre
Bayen, Alexandre M.
Saint-Pierre, Patrick
2011

Mobile Transit Trip Planning with Real-Time Data

Jariyasunant, Jerald
Work, Daniel B.
Kerkez, Branko
Bayen, Alexandre M.
2011

In this article, we describe the development of a transit trip planner (TTP) for mobile devices called Transitr, and evaluate its performance. The system predicts the shortest paths betweenany two points in the transit network using real-time information provided by a third party busarrival prediction system, relying on GPS equipped transit vehicles. Users submit their originand destination through a map-based iPhone application, or through a JavaScript enabled web browser. A server implementing a dynamic K-shortest paths algorithm with predicted link travel times returns personalized...