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 formula to compute these solutions. We illustrate the results with three examples: the computation of the hybrid components of a Lighthill-Whitham-Richards equation; a velocity control policy for a highway system; a data assimilation problem using Lagrangian measurements generated from NGSIM traffic data.
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Claudel, C.G., Bayen, A.M. (2008). Solutions to Switched Hamilton-Jacobi Equations and Conservation Laws Using Hybrid Components. In: Egerstedt, M., Mishra, B. (eds) Hybrid Systems: Computation and Control. HSCC 2008. Lecture Notes in Computer Science, vol 4981. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78929-1_8
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DOI: https://doi.org/10.1007/978-3-540-78929-1_8
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