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Synthesis of optimal control for systems described by a hyperbolic equation. (Russian) Zbl 0569.49014

The author deals with the optimal control problem for the minimum of the functional \(J(u)=| w(T)-y_ 0|^ 2_ 0+| w'(T)-y_ 1|^ 2_ 0\), \(u\in U_ R\), under conditions \(w''+b(t)w'+Aw+c(t)w=u(t)+f^ 0(t)\), \(t_ 0<t\leq T\), \(w(t_ 0)=\phi_ 0\), \(w'(t_ 0)=\phi_ 1\), where A is a linear selfadjoint coercive operator in a Hilbert space H. The differentiability of the functional J in the space \(L_ 2(t_ 0,T;H)\) is proved, necessary and sufficient optimality and controllability conditions are derived.
Reviewer: I.Bock

MSC:

49K20 Optimality conditions for problems involving partial differential equations
49J50 Fréchet and Gateaux differentiability in optimization
93B05 Controllability
35B37 PDE in connection with control problems (MSC2000)
35L10 Second-order hyperbolic equations
93B50 Synthesis problems
47B25 Linear symmetric and selfadjoint operators (unbounded)
46C99 Inner product spaces and their generalizations, Hilbert spaces
93C05 Linear systems in control theory
93C20 Control/observation systems governed by partial differential equations
49K27 Optimality conditions for problems in abstract spaces
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