an:01752617
Zbl 1008.49014
Arguchintsev, A. V.; Krutikova, O. A.
Optimization of semilinear hyperbolic systems with smooth boundary controls
EN RU
Russ. Math. 45, No. 2, 1-9 (2001); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2001, No. 2, 3-12 (2001).
00086066
2001
j
49K20 49M05 35Q93 35L40
optimal control; semilinear hyperbolic systems; necessary optimality condition; numerical method
The authors consider the following optimal control problem for semilinear hyperbolic systems with smooth boundary controls \(u(s)\):
\[
J(u)= \int_S \varphi(x(s, t_1), s)\,ds+ \iint_P F(x,s,t)\,ds\,dt\to \text{minimum},
\]
\[
{\partial x\over\partial t}+ A(s,t) {\partial x\over\partial s}= f(x,s,t),
\]
\[
x(s, t_0)= p(u(s), s),\quad x^+(s_0, t)= M(t) x^-(s_0, t)+ g^{(1)}(t),
\]
\[
x^-(s_1, t)= N(t) x^+(s_1, t)+ g^{(2)}(t).
\]
For these problems, a necessary optimality condition is derived and a numerical method is given, which is based on the optimality condition. A numerical test is given.
Hans Benker (Merseburg)