Exact controllability of the Euler-Bernoulli equation with controls in the Dirichlet and Neuman boundary conditions: a nonconservative case


This paper considers the Euler-Bernoulli problem with boundary controls g1, g2 in the Dirichlet and Neumann boundary conditions, respectively. Several exact controllability results are shown, including the following. The problem is exactly controllable in an arbitrarily short time T>0 in the space (of maximal regularity) H-1(Ω) × V′, V as specified, (i) with boundary controls g1 member of L2(Σ), g2≡0 under some geometrical conditions on Ω; (ii) with boundary controls g1 member of L2(Σ) and g2 member of L2(0, T; H-1(Γ)) without geometrical conditions on Ω. A direct approach is given, based on an operator model for the problem and on multiplier techniques.

Publication Title

SIAM Journal on Control and Optimization