ITS Berkeley

Solutions to Switched Hamilton-Jacobi Equations and Conservation Laws Using Hybrid Components

Claudel, Christian G.
Bayen, Alexandre M.
Egerstedt, Magnus
Mishra, Bud
2008

We investigate a class of hybrid systems driven by partial differential equations for which the infinite dimensional state can switch in time and in space at the same time. We consider a particular class of such problems (switched Hamilton-Jacobi equations) and define hybrid components as building blocks of hybrid solutions to such problems, using viability theory. We derive sufficient conditions for well-posedness of such problems, and use a generalized Lax-Hopf formula to compute these solutions. We illustrate the results with three examples: the computation of the hybrid components of a...

A Framework for Analyzing the Sensitivity of Traffic Data Quality to Sensor Location and Spacing: 15th World Congress on Intelligent Transport Systems and ITS America Annual Meeting 2008

Margulici, J.D.
Ban, Xuegang (Jeff)
Bayen, Alexander M.
Chu, Lianyu
2008

This paper presents a framework and tools developed to study the sensitivity of traffic data quality to detectors location and spacing. Our ultimate objective is to formulate generalized detector deployment guidelines that are based on the functional needs of practitioners, and for which funding can be objectively justified. Our approach consists in using trajectory sets obtained from field experiments and traffic simulation models as ground truth, and to run a traffic detector model from which we extract information that would normally be available to practitioners. Ground truth...

Automotive Cyber Physical Systems in the Context of Human Mobility

Work, Daniel B.
Bayen, Alexandre M.
Jacobson, Quinn
2008

We discuss the limitations of the current automotive Cyber Physical System (CPS). Its vehicle-centric view only provides partial information about the surrounding environment, it is not well suited to address the needs of embedded humans in the system, and it moves too slowly to keep pace with other technologies. In the larger context of human mobility, the automotive CPS must become more open and flexible, new human mobility models need to be developed, and the key issue of privacywill need to be addressed to protect increasingly important and prevalent location based data.

Dirichlet Problems for some Hamilton–Jacobi Equations with Inequality Constraints

Aubin, Jean-Pierre
Bayen, Alexandre M.
Saint-Pierre, Patrick
2008

The value function of Mayer’s problem arising in optimal control is investigated, and lower semicontinuous solutions of the associated Hamilton–Jacobi–Bellman equation are defined in three (equivalent) ways. Under quite weak assumptions about the control system, the value function is the unique solution. Moreover, it is stable with respect to perturbations of the control system and the cost. It coincides with the viscosity solution whenever it is continuous.

Invariance-Preserving Abstractions of Hybrid Systems: Application to User Interface Design

Oishi, Meeko
Mitchell, Ian
Bayen, Alexander M.
Tomlin, Claire J.
2008

Hybrid systems combine discrete state dynamics which model mode switching, with continuous state dynamics which model physical processes. Hybrid systems can be controlled by affecting both their discrete mode logic and continuous dynamics: in many systems, such as commercial aircraft, these can be controlled both automatically and using manual control. A human interacting with a hybrid system is often presented, through information displays, with a simplified representation of the underlying system. This user interface should not overwhelm the human with unnecessary information, and thus...

Virtual Trip Lines for Distributed Privacy-Preserving Traffic Monitoring

Hoh, Baik
Gruteser, Marco
Herring, Ryan
Ban, Jeff
Work, Daniel
Bayen, Alexander M.
2008

Automotive traffic monitoring using probe vehicles with Global Positioning System receivers promises significant improvements in cost, coverage, and accuracy. Current approaches, however, raise privacy concerns because they require participants to reveal their positions to an external traffic monitoring server. To address this challenge, we propose a system based on virtual trip lines and an associated cloaking technique. Virtual trip lines are geographic markers that indicate where vehicles should provide location updates. These markers can be placed to avoid particularly privacy...

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...