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Solution of the problem of optimal control of initial-boundary value conditions of a hyperbolic system on the basis of exact increment formulas. (English. Russian original) Zbl 1060.49018
Russ. Math. 46, No. 12, 21-27 (2002); translation from Izv. Vyssh. Uchebn. Zaved. Mat. 2002, No. 12, 23-29 (2002).
The paper considers an optimal control problem governed by a linear hyperbolic system in the rectangle $$(x,t)\in D= [x_1, x_2]\times [t_0, T]$$ with control in the boundary conditions and a linear cost functional. The specific of the problem is that the boundary conditions are given in the form of ordinary differential equations (with respect to the time variable) that contain controls. The author gives formulae for the increment of the cost functional by reducing the original problem to an optimal control problem for ordinary differential equations on the boundary of the rectangle $$D$$.
##### MSC:
 49K20 Optimality conditions for problems involving partial differential equations 35L50 Initial-boundary value problems for first-order hyperbolic systems 49M05 Numerical methods based on necessary conditions