Abstract
In this paper we consider the optimal control problem for a system of first-order hyperbolic equations. The right-hand side of this system is determined by a control system of ordinary differential equations. Admissible controls belong to the class of smooth functions. We obtain an optimality condition and propose a general scheme of improvement methods for the mentioned problem.
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References
N. D. Demidenko, V. I. Potapov, and Yu. I. Shokin, Modeling and Optimization of Systems with Distributed Parameters (Nauka, Novosibirsk, 2006) [in Russian].
A. V. Arguchintsev, Optimal Control for Hyperbolic Systems (Fizmatlit, Moscow, 2007) [in Russian].
B. L. Rozhdestvenskii and N. N. Yanenko, Systems of Quasilinear Equations and Their Applications to Gas Dynamics (Nauka, Moscow, 1978) [in Russian].
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Original Russian Text © A.V. Arguchintsev and V.P. Poplevko, 2009, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2009, No. 7, pp. 71–76.
(Submitted byV. A. Srochko)
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Arguchintsev, A.V., Poplevko, V.P. Optimization of one class of hyperbolic systems with smooth controls. Russ Math. 53, 60–64 (2009). https://doi.org/10.3103/S1066369X0907007X
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DOI: https://doi.org/10.3103/S1066369X0907007X