Optimal control of Goursat-Darboux systems in domains with curvilinear boundaries

2005/09/03 by S. A. Belbas, Belbas, S. A.
Mathematics · #35L70 #35R30 #49J20 #49K20 #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC) #math.AP #math.OC #msc:35L70 #msc:35R30 #msc:49J20 #msc:49K20

paper · pdf · doi:10.48550/arxiv.math/0509070

50 pages

arxiv created 2005/09/03 · arxiv updated 2009/12/01

Abstract

We derive necessary conditions for optimality in control problems governed by hyperbolic partial differential equations in Goursat-Darboux form. The conditions consist of a set of Hamiltonian equations in Goursat form, side conditions for the Hamiltonian equations, and an extremum principle akin to Pontryagin's maximum principle. The novel ingredient is that the domain over which the optimal control problem is posed is not rectangular. The non-rectangular nature of the domain affects the optimality conditions in a substantial way.

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