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

• Autorzy: Gavrilov V. S. , Sumin M. I.
• Języki publikacji: EN

Abstrakty

EN

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 described 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.

Słowa kluczowe

EN

sequential optimization; maximum principle for minimizing sequences; semilinear hyperbolic partial differential equations; pointwise in time state constraints; boundary control; value function; sensitivity; normality; regularity; Radon measures; twoparameter needle variation of controls

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2014
• Tom: Vol. 43, no. 2
• Strony: 183--226
• Opis fizyczny: Bibliogr. 47 poz.

Twórcy

autor

Gavrilov V. S.

• Mathematical Department, Nizhnii Novgorod State University, Gagarin street 23, 603950 Nizhnii Novgorod, Russia

autor

Sumin M. I.

• Mathematical Department, Nizhnii Novgorod State University, Gagarin street 23, 603950 Nizhnii Novgorod, Russia

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