16:10
Optimal Control of a Coupled System of a Vehicle Transporting a Fluid Subject to Shallow Water Equations
Dr. Sven-Joachim Kimmerle | Universität der Bundeswehr München | Germany
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Authors:
Dr. Sven-Joachim Kimmerle | Universität der Bundeswehr München | Germany
Dr. Matthias Gerdts | Universität der Bundeswehr München | Germany
We consider the optimal control of a vehicle transporting an open fluid basin as load. The motion of the fluid is modeled by the non-linear hyperbolic shallow water (Saint-Venant) equations, while the vehicle dynamics are described by Newtonʼs equations of motion. The fluid basin is mounted to the vehicle by a spring-damper element. The system may be controlled by the acceleration of the vehicle.
This leads to an optimal control problem with a coupled system of partial differential equations (PDEs) and ordinary differential equations (ODEs). The PDEs and ODEs are fully coupled by boundary conditions and force terms.
We derive necessary optimality conditions rigorously and solve by a first-optimize-then-discretize approach, using Newton's method. In particular, we employ a certain globalization strategy for semi-smooth Newton methods in Hilbert spaces here. As well we consider a first-discretize-then-optimize approach for the particular case of time optimal control. The Saint-Venant equations are discretized by means of a Lax-Friedrich scheme, involving an artificial viscosity.
Finally, we consider further examples (an elastic crane-trolley-load system, a quarter car model with free road contact) for fully coupled systems of PDEs and ODEs. We discuss their particular features and classify our problem within this context.
16:30
On the stabilization of parabolic equations by a finite number of actuators
Dr. Sergio Rodrigues | RICAM | Austria
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Dr. Sergio Rodrigues | RICAM | Austria
duy phan | Germany
We present some results concerning the stabilizability of a parabolic-like equation by means of a finite number of a priori given actuators. The actuators may be supported in a small subset either of the interior or of the boundary of the domain.
16:50
Optimal Length Control of Thermoelastic Material
M. Sc. Chathuri Fernando | Technische Universität Kaiserslautern | Germany
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M. Sc. Chathuri Fernando | Technische Universität Kaiserslautern | Germany
The optimal control of free boundary value problems is a newly interesting topic among researchers. Here, we present both analytic and numerical studies of one dimensional optimal distributed heat control of a thermoelastic material with applications in the glass manufacturing. The goal is to achieve a desired shape of the domain by minimizing an appropriate cost functional. Hence, a constrained optimization problem solved where the constraints are given by a nonlinear parabolic/ elliptic PDE system. A suitable PDE model was derived by considering heat equation together with the equilibrium equation of motion for small deformations in Lagrangian framework. First, we discuss the existence and uniqueness of the bounded states and optimal control under certain regularity assumptions and then use standard techniques to derive the first order optimality system. Second, we present numerical results for the problem where we used well-known gradient based optimization algorithms available.
17:10
Optimal Vaccination Strategies for Dengue-Fever
Prof. Dr. Kurt Chudej | Universitaet Bayreuth | Germany
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Prof. Dr. Kurt Chudej | Universitaet Bayreuth | Germany
Dengue fever is known to be present e.g. in Asia (China, Singapore, Brazil, …). It is carried over by the asian tiger mosquito between infected humans. In 1979 this mosquito was found for the first time outside Asia in Albania. The list of European countries in which it is found gets longer every year. The asian tiger mosquito was found since 2007 in Albania, Serbia, France, Italy, Slowenia, Spain and Switzerland among other countries. At least since 2007 the asian tiger mosquito is detectable in Freiburg im Breisgau (South Germany) and since 2010 in South Tyrol. Along the transit highway between Rosenheim and Kufstein adult asian tiger mosquitos were found in 2012. In 2016 asian tiger mosquitos were also found in Regensburg. The global warming increases the risk of the establishment of stable Asian tiger mosquito populations in Germany. Up to now dengue fever cases in Germany could be tracked back to an infection abroad. But this may change. A vaccine against dengue fever is currently in development.
We present numerical results for optimal vaccination strategies for a hypothetical outbreak of dengue fever in the region around Freiburg im Breisgau based on a mathematical optimal control model.