Andrei Fursikov
Moskow
EXACT CONTROLLABILITY AND FEEDBACK STABILIZATION
FOR PARABOLIC EQUATIONS AND FOR NAVIER-STOKES SYSTEM.
Exact controllability problem for evolution
equations indicated in the title is formulated as follows:
Let a solution $w(t,x), t\in (0,T), x\in G$ of this
equation be given where $G$ is a bounded domain. Then
for a prescribed initial value $v_0(x)\ne w(0,x) $ one
have to find a boundary control $u(t,x), t\in (0,T),
x\in \partial G$ such that the solution $v(t,x)$ of
the boundary value problem supplied with initial and
boundary conditions $v_0$ and $u$ satisfies: $v(T,x)=w(T,x)$
Existence theorem for exact controllability problem will be
discussed in the course.
We will show that exact controllability problem is ill-posed
and therefore its calculation or ingeneering realization
is difficult. We will consider so called stabilization problem
which setting is close to exact controllability formulation.
But stabilization problem will be solved with help of feedback
control that damps fluctuations arising in calculations. This
indicate on well-posedness of proposed resolving construction.
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