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

Authors:
Christian G. Claudel;Alexandre M. Bayen
Affiliations:
Electrical Engineering and Computer Sciences,;Systems Engineering, Civil and Environmental Engineering, University of California, Berkeley, Berkeley, 94720-1710
Venue:
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Year:
2008

Citing 3
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HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control

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Abstract

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 formulato compute these solutions. We illustrate the results with three examples: the computation of the hybrid components of a Lighthill-Whitham-Richardsequation; a velocity control policy for a highway system; a data assimilation problem using Lagrangian measurements generated from NGSIM traffic data.