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Optimization of one class of hyperbolic systems with smooth controls. (English. Russian original) Zbl 1180.49021
Russ. Math. 53, No. 7, 60-64 (2009); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2009, No. 7, 71-76 (2009).
Summary: 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.

MSC:
49K20 Optimality conditions for problems involving partial differential equations
35L04 Initial-boundary value problems for first-order hyperbolic equations
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References:
[1] N. D. Demidenko, V. I. Potapov, and Yu. I. Shokin, Modeling and Optimization of Systems with Distributed Parameters (Nauka, Novosibirsk, 2006) [in Russian].
[2] A. V. Arguchintsev, Optimal Control for Hyperbolic Systems (Fizmatlit, Moscow, 2007) [in Russian].
[3] 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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