Tracking control of 1D scalar conservation laws in the presence of shocks
Lecaros R, Zuazua E (2014)
Publication Type: Book chapter / Article in edited volumes
Publication year: 2014
Publisher: Springer International Publishing
Edited Volumes: Trends in Contemporary Mathematics
Series: Springer INdAM Series
Book Volume: 8
Pages Range: 195-219
DOI: 10.1007/978-3-319-05254-0_15
Abstract
We analyze a model tracking problem for a 1D scalar conservation law. It consists in optimizing the initial datum so to minimize a weighted distance to a given target during a given finite time horizon. Even if the optimal control problem under consideration is of classical nature, the presence of shocks is an impediment for classical methods, based on linearization, to be directly applied. We adapt the so-called alternating descent method that exploits the generalized linearization that takes into account both the sensitivity of the shock location and of the smooth components of solutions. This method was previously applied successfully on the inverse design problem and that of identifying the nonlinearity in the equation. The efficiency of the method in comparison with more classical discrete methods is illustrated by several numerical experiments.
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APA:
Lecaros, R., & Zuazua, E. (2014). Tracking control of 1D scalar conservation laws in the presence of shocks. In Vincenzo Ancona, Elisabetta Strickland (Eds.), Trends in Contemporary Mathematics. (pp. 195-219). Springer International Publishing.
MLA:
Lecaros, Rodrigo, and Enrique Zuazua. "Tracking control of 1D scalar conservation laws in the presence of shocks." Trends in Contemporary Mathematics. Ed. Vincenzo Ancona, Elisabetta Strickland, Springer International Publishing, 2014. 195-219.
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