ITS Berkeley

Guaranteed Bounds for Traffic Flow Parameters Estimation Using Mixed Lagrangian-Eulerian Sensing

Claudel, Christian G.
Bayen, Alexandre M.
2008

This article proposes a new method combining convex optimization and viability theory for estimating traffic flow conditions on highway segments. Traffic flow is modeled by a Hamilton-Jacobi equation. Using a Lax-Hopf formula, we formulate the necessary and sufficient conditions for a mixed boundary and internal conditions problem to be well posed. The well-posedness conditions result in a system of linear inequalities, which enables us to compute upper and lower bounds on traffic flow parameters as the solution to a linear program. We illustrate the capabilities of the method with a data...

Stability Analysis of Linear Hyperbolic Systems with Switching Parameters and Boundary Conditions

Amin, Saurabh
Hante, Falk M.
Bayen, Alexandre M.
2008

We study asymptotic stability of an infinite dimensional system that switches between a finite set of modes. Each mode is governed by a system of one-dimensional, linear, hyperbolic partial differential equations on a bounded space interval. The switching system is fairly general in that the space dependent system matrix functions as well as the boundary conditions may switch in time. For the case in which the switching occurs between subsystems in canonical diagonal form, we provide two sets of sufficient conditions for asymptotic stability under arbitrary switching signals. These results...

Feed-Forward River Flow Control Using Differential Flatness

Di Meglio, Florent
Rabbani, Tarek
Litrico, Xavier
Bayen, Alexandre M.
2008

The rarefaction of global water resources is a motivation for research on automation of management of water distribution systems. Large amounts of fresh water are lost due to poor management of open-channel systems. This article focuses on the management of such canals which are used to convey water from the resource (generally a dam located upstream) to a specific downstream location. Due to the fluctuations of water needs, water demand changes with time. This change in demand calls for the efficient operation of the open-channel systems to avoid overflows and to supply desired flow rates...

Ensemble Kalman Filter Based State Estimation in 2D Shallow Water Equations Using Lagrangian Sensing and State Augmentation

Tossavainen, Olli‐Pekka
Percelay, Julie
Tinka, Andrew
Wu, Qingfang
Bayen, Alexander M.
2008

We present a state estimation method for two-dimensional shallow water equations in rivers using Lagrangian drifter positions as measurements. The aim of this method is to compensate for the lack of knowledge of upstream and downstream boundary conditions in rivers that causes inaccuracy in the velocity field estimation by releasing drifters equipped with GPS receivers. The drifters report their positions and thus provide additional information of the state of the river. This information is incorporated into shallow water equations by using Ensemble Kalman Filtering (EnKF). The proposed...

Convex Formulations of Aggregate Network Air Traffic Flow Optimization Problems

Work, Daniel B.
Bayen, Alexandre M.
2008

The problem of regulating air traffic in the en route airspace of the national airspace system is studied using an Eulerian network model to describe air traffic flow. The evolution of traffic on each edge of the network is modeled by a modified Lighthill-Whitham-Richards partial differential equation. We pose the problem of optimal traffic flow regulation as a continuous optimization program in which the partial differential equation appears in the constraints. The equation is transformed with a variable change which removes t nonlinearity in the control variables and enables us to use...

Convex Formulations of Air Traffic Flow Optimization Problems

Work, Daniel B.
Bayen, Alexandre M.
2008

The problem of regulating air traffic in the en route airspace of the National Airspace System is studied using a Eulerian network model to describe air traffic flow. The evolution of traffic on each edge of the network is modeled by a modified Lighthill-Whitham-Richards partial differential equation. The equation is transformed with a variable change, which makes it linear and enables us to use linear finite difference schemes to discretize the problem. We pose the problem of optimal traffic flow regulation as a continuous optimization program in which the partial differential equation...

An Ensemble Kalman Filtering Approach to Highway Traffic Estimation Using GPS Enabled Mobile Devices

Work, Daniel B.
Tossavainen, Olli‐Pekka
Blandin, Sébastien
Bayen, Alexandre M.
Iwuchukwu, Tochukwu
Tracton, Kenneth
2008

Traffic state estimation is a challenging problem for the transportation community due to the limited deployment of sensing infrastructure. However, recent trends in the mobile phone industry suggest that GPS equipped devices will become standard in the next few years. Leveraging these GPS equipped devices as traffic sensors will fundamentally change the type and the quality of traffic data collected on large scales in the near future. New traffic models and data assimilation algorithms must be developed to efficiently transform this data into usable traffic information. In this work, we...

Boundary Data Reconstruction for Open Channel Networks Using Modal Decomposition

Wu, Q.
Litrico, X.
Bayen-Poisson, Aurélie
2008

This article presents a method to estimate flow variables for an open channel network governed by first-order, linear hyperbolic partial differential equations and subject to periodic forcing. The selected external boundary conditions of the system are defined as the model input; the flow properties at internal locations, as well as the other external boundary conditions, are defined as the output. A spatially-dependent transfer matrix in the frequency domain is constructed to relate the model input and output. A data reconciliation technique efficiently eliminates the error in the...

Preface

Bastin, George
Bayen, Alexandre M.
2009

Management of canal networks at the age of information technology. With the miniaturization of sensors and their decreasing costs, the paradigm of instrumentation of the built infrastructure and the environment has now been underway for several years, leading to numerous successful and sometimes spectacular realizations such as the instrumentation of the Golden Gate with wire- less sensors a few years ago. The convergence of communication, control and sensing on numerous platforms including multi-media platforms has enabled engineers to augment physical infrastructure systems with an...

Réconciliation de Données d'un Réseau Hydraulique à Surface Libre à L'aide de la Décomposition Modale

Wu, Qingfang
Litrico, Xavier
Bayen, Alexandre M.
2009

Data reconciliation of an open channel flow network using modal decomposition.