ITS Berkeley

Computation of Solutions to the Moskowitz Hamilton-Jacobi-Bellman Equation Under Viability Constraints

Bayen, Alexandre M.
Claudel, Christian
Saint-Pierre, Patrick
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), based on a Lax-Hopf formula. The capture basin algorithm is derived and implemented to perform numerical computations of constrained solutions. The rate of convergence of this first order algorithm is assessed experimentally using an analytical benchmark problem. Finally, its performance is measured with highway data obtained for interstate 180 in California.

Parameter Identification for the Shallow Water Equation Using Modal Decomposition

Wu, Qingfang
Amin, Saurabh
Munier, Simon
Bayen, Alexandre M.
Litrico, Xavier
Belaud, Gilles
2007

A parameter identification problem for systems governed by first-order, linear hyperbolic partial differential equations subjected to periodic forcing is investigated. The problem is posed as a PDE constrained optimization problem with data of the problem given by the measured input and output variables at the boundary of the domain. By using the governing equations in the frequency domain, a spatially dependent transfer matrix relating the input variables to the output variables is obtained. It is shown that by considering a finite number of dominant oscillatory modes of the input, an...

On Stability of Switched Linear Hyperbolic Conservation Laws with Reflecting Boundaries

Amin, Saurabh
Hante, Falk M.
Bayen, Alexandre M.
Egerstedt, Magnus
Mishra, Bud
2008

We consider stability of an infinite dimensional switching system, posed as a system of linear hyperbolic partial differential equations (PDEs) with reflecting boundaries, where the system parameters and the boundary conditions switch in time. Asymptotic stability of the solution for arbitrary switching is proved under commutativity of the advective velocity matrices and a joint spectral radius condition involving the boundary data.

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...