A theorem on the existence of an optimal control for the Goursat-Darboux problem without convexity assumptions (Q2710700)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A theorem on the existence of an optimal control for the Goursat-Darboux problem without convexity assumptions |
scientific article |
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24 July 2001
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optimal control
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Goursat-Darboux problem
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nonconvex problem
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wave equation
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state constraints
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multivalued integrals
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A theorem on the existence of an optimal control for the Goursat-Darboux problem without convexity assumptions (English)
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The author studies the optimal control of the wave equation with Goursat-Darboux boundary conditions, in the presence of control and state constraints with a nonconvex integrand. This result extends previous existence results due to \textit{M. B. Suryanarayana} [J. Optimization Theory Appl. 19, 47-61 (1976; Zbl 0305.49005)] and to \textit{A. Bressan} and \textit{F. Flores} [J. Math. Anal. Appl. 189, No. 2, 315-334 (1995; Zbl 0828.49005)]. The proof is based on properties of multivalued integrals. The novelty is the introduction of a new type of constraints.
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