Sequential optimization for semilinear divergent hyperbolic equation with a boundary control and state inequality constraint

An optimal control problem with a state constraint of inequality type and with dynamics described by a semilinear hyperbolic equation in divergence form with the non-homogeneous boundary condition of the third kind is considered. The state constraint contains a functional parameter that belongs to t...

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Bibliographic Details
Published in:Control and cybernetics 2014-04, Vol.43 (2), p.183
Main Authors: Gavrilov, Vladimir S, Sumin, Mikhail I
Format: Article
Language:English
Subjects:
Differential equations, Partial
Inequalities (Mathematics)
Mathematical optimization
Mathematical research
Sequences (Mathematics)
Online Access:Get full text
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Summary:An optimal control problem with a state constraint of inequality type and with dynamics described by a semilinear hyperbolic equation in divergence form with the non-homogeneous boundary condition of the third kind is considered. The state constraint contains a functional parameter that belongs to the class of continuous functions and occurs as an additive term. We study the properties of solutions of linear hyperbolic equations in divergence form with measures in the original data and compute the first variations of functionals on the basis of a so-called two-parameter needle variation of controls. We consider the necessary conditions for minimizing sequences in an optimal control problem with a pointwise in time state constraint of inequality type and with dynamics de scribed by a semilinear hyperbolic equation in divergence form with the non-homogeneous boundary condition of the third kind. For the parametric optimization problem, we also consider regularity and normality conditions stipulated by the differential properties of its value function.
ISSN:0324-8569