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Paper details
Number 4 - December 1996
Volume 6 - 1996
An example of non-existence of a cone approximation to the set of feasible states for an optimal control problem
Uldis Raitums
Abstract
The paper considers optimal control problems for linear elliptic systems with a standard set S of admissible controls σ. In the case where the principal part of the operator depends on controls, it is shown that the set Z(S) of all solutions u(σ) of the state equations with σ ∈ S cannot be approximated, in general, by cones, i.e. for a given with σ0 ∈ S there is, in general, neither element h nor family {σε} ⊂ S such that u(σε) = u(σ0) + εh + o(ε) as ε → 0.
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