ITS Berkeley

Mixed Initial-Boundary Value Problems for Scalar Conservation Laws: Application to the Modeling of Transportation Networks

Strub, Issam S.
Bayen, Alexandre M.
Hespanha, João P.
Tiwari, Ashish
2006

This article proves the existence and uniqueness of a weak solution to a scalar conservation law on a bounded domain. A weak formulation of hybrid boundary conditions is needed for the problem to be well posed. The boundary conditions are represented by a hybrid automaton with switches between the modes determined by the direction of characteristics of the system at the boundary. The existence of the solution results from the convergence of a Godunov scheme derived in this article. This weak formulation is written explicitly in the context of a strictly concave flux function (relevant for...

MILP Control of Aggregate Eulerian Network Airspace Models

Robelin, C.-A.
Sun, Dengfeng
Wux, Guoyuan
Bayen, Alexandre M.
2006

A new Eulerian model of airspace is derived and applied to high altitude traffic for a full air traffic control center of the National Airspace System. The Eulerian model is reduced to a linear time invariant dynamical system, in which the state is a vector of aggregate aircraft counts. The model is validated against ASDI data and applied to the Oakland airspace. The problem of controlling sector aircraft count is posed as an integer program, in which the dynamical system appears in the constraints. To improve the computational time of calculating the solution, the integer program is...

Sensing by Proxy: Occupancy Detection Based on Indoor CO2 Concentration

Jin, Ming
Bekiaris-Liberis, Nikolaos
Weekly, Kevin
Spanos, Costas
Bayen, Alexandre
2015

Sensing by proxy, as described in this study, is a sensing paradigm which infers latent factors by “proxy” measurements based on constitutive models that exploit the spatial and physical features in the system. In this study, we demonstrate the efficiency of sensing by proxy for occupancy detection based on indoor CO2 concentration. We propose a link model that relates the proxy measurements with unknown human emission rates based on a data-driven model which consists of a coupled Partial Differential Equation (PDE) – Ordinary Differential Equation (ODE) system. We report on several...

Real-Time Video Detection of Falls in Dementia Care Facility and Reduced Emergency Care

Xiong, Glen
Bayen, Eleonore
Nickels, Shirley
Subramaniam, Raghav
2019

An artificial intelligence-enabled video fall detection system using visual science reduced emergency department visits by 80% in 6 communities over 3 months.

Control for Societal-scale Challenges: Road Map 2030

Alleyne, Andrew
Allgöwer, Frank
Ames, Aaron D.
Bayen, Alexandre M.
2023

The world faces some of its greatest challenges of modern time and how we address them will have a dramatic impact on the life for generations to come. Simultaneously, control systems, consisting of information enriched by various degrees of analytics followed by decision-making, are pervading a variety of sectors, not only in engineering but beyond, into financial services, socio-economic analysis, entertainment and sports, and political and social sciences. Increased levels of automation are sought after in various sectors and being introduced into new domains. All of these advances and...

Adjoint-based Control of a New Eulerian Network Model of Air Traffic Flow

Bayen, A.M.
Raffard, R.L.
Tomlin, C.J.
2006

An Eulerian network model for air traffic flow in the National Airspace System is developed and used to design flow control schemes which could be used by Air Traffic Controllers to optimize traffic flow. The model relies on a modified version of the Lighthill-Whitham-Richards (LWR) partial differential equation (PDE), which contains a velocity control term inside the divergence operator. This PDE can be related to aircraft count, which is a key metric in air traffic control. An analytical solution to the LWR PDE is constructed for a benchmark problem, to assess the gridsize required to...

Continuous Adjoint Method for Air Traffic Flow Management

Strub, Issam S.
Bayen, Alexandre M.
2006

This article develops a model of air traffic flow using an Eulerian description with hyperbolic partial differential equations. Existence and uniqueness (well-posedness) of a solution to the system of partial differential equations on a network is established. Subsequently, an optimal control problem is studied with the junction coefficients as control variables. We use a continuous adjoint approach and we implement it on a network with 16 links and 5 junctions, demonstrating the computational efficiency of this method

Viability-Based Computations of Solutions to the Hamilton-Jacobi-Bellman Equation

Bayen, Alexandre M.
Claudel, Christian
Saint-Pierre, Patrick
Bemporad, Alberto
Bicchi, Antonio
2007

This article proposes a new capture basin algorithm for computing the numerical solution of a class of Hamilton-Jacobi-Bellman (HJB) partial differential equations (PDEs) [3], based on a Lax-Hopf formula [2]. The capture basin algorithm is derived and implemented to perform numerical computations. Its performance is measured with highway data obtained for interstate I80 in California.

Aircraft Autolander Safety Analysis Through Optimal Control-Based Reach Set Computation

Bayen, Alexandre M.
Mitchell, Ian M.
Oishi, Meeko
Tomlin, Claire J.
2007

Traffic Flow Reconstruction Using Mobile Sensors and Loop Detector Data

Herrera, Juan C.
Bayen, Alexandre M.
2007

In order to develop efficient control strategies to improve traffic conditions on freeways, it is necessary to know the state of the freeway at any point in time and space. Using data collected from stationary detectors –such as loop detector stations– the density field can be currently reconstructed to a certain accuracy. Unfortunately, deploying this type of infrastructure is expensive, and its reliability varies. This article proposes and investigates new algorithms that make use of data provided by mobile sensors, in addition to that collected by stationary detectors, to reconstruct...