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Controllability of a slowly rotating Timoshenko beam

Martin Gugat — 2001

ESAIM: Control, Optimisation and Calculus of Variations

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...

Controllability of a slowly rotating Timoshenko beam

Martin Gugat — 2010

ESAIM: Control, Optimisation and Calculus of Variations

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...

Existence of classical solutions and feedback stabilization for the flow in gas networks

Martin GugatMichaël Herty — 2011

ESAIM: Control, Optimisation and Calculus of Variations

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.

-Norm minimal control of the wave equation: on the weakness of the bang-bang principle

Martin GugatGunter Leugering — 2008

ESAIM: Control, Optimisation and Calculus of Variations


For optimal control problems with ordinary differential equations where the L -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...

Existence of classical solutions and feedback stabilization for the flow in gas networks

Martin GugatMichaël Herty — 2011

ESAIM: Control, Optimisation and Calculus of Variations

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.

Conservation law constrained optimization based upon front-tracking

Martin GugatMichaël HertyAxel KlarGunter Leugering — 2006

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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...

Conservation law constrained optimization based upon Front-Tracking

Martin GugatMichaël HertyAxel KlarGunter Leugering — 2007

ESAIM: Mathematical Modelling and Numerical Analysis

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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