Consider a Timoshenko beam that is clamped to an axis perpendicular to the axis of the beam. We study the problem to move the beam from a given initial state to a position of rest, where the movement is controlled by the angular acceleration of the axis to which the beam is clamped. We show that this problem of controllability is solvable if the time of rotation is long enough and a certain parameter that describes the material of the beam is a rational number that has an even numerator and an odd...
Consider a Timoshenko beam that is clamped to an axis perpendicular to
the axis of the beam.
We study the problem to move the beam from a given initial state
to a position of rest, where the movement is controlled by the angular
acceleration of the axis to which the beam is clamped.
We show that this problem of controllability is solvable if the time of
rotation is long enough and a certain parameter
that describes the material of the beam
is a rational number
that has an even numerator and an...
We consider the flow of gas through pipelines controlled by a compressor station. Under a subsonic flow assumption we prove the existence of classical solutions for a given finite time interval. The existence result is used to construct Riemannian feedback laws and to prove a stabilization result for a coupled system of gas pipes with a compressor station. We introduce a Lyapunov function and prove exponential decay with respect to the
-norm.
For optimal control problems with ordinary
differential equations where the -norm of the control is
minimized, often bang-bang principles hold. For systems that are
governed by a hyperbolic partial differential equation, the
situation is different:
even if a weak form of the bang-bang principle still holds for the wave equation,
it implies no restriction on the form of the optimal control.
To illustrate that
for the Dirichlet boundary control of the wave equation
in general not even feasible...
We consider the flow of gas through pipelines controlled by a compressor
station. Under a subsonic flow assumption we prove the existence
of classical solutions for a given finite time interval.
The existence result is used to construct Riemannian feedback laws and
to prove a stabilization result for a coupled system of gas pipes with a compressor
station. We introduce a Lyapunov function and prove exponential decay
with respect to the
-norm.
We consider models based on conservation laws. For the optimization of such systems, a sensitivity analysis is essential to determine how changes in the decision variables influence the objective function. Here we study the sensitivity with respect to the initial data of objective functions that depend upon the solution of Riemann problems with piecewise linear flux functions. We present representations for the one–sided directional derivatives of the objective functions. The results can be used...
We consider models based on conservation laws. For the optimization
of such systems, a sensitivity analysis is essential to determine
how changes in the decision variables influence the objective
function. Here we study the sensitivity with respect to the initial
data of objective functions that depend upon the solution of Riemann
problems with piecewise linear flux functions. We present
representations for the one–sided directional derivatives of the
objective functions. The results can be used...
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