The interplay of control and Deep Learning By Borjan Geshkovski   It is superfluous to state […]

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Derivation of the pressure function Code: Files to run: nocircle.m, onecircle.m or twocircles.m   1 Introduction This post presents the results of my Bachelor thesis about the modeling and implementation of gas networks at stationary states. Using the isothermal Euler equations to describe the gas flow […]
Uniform Turnpike Property 1 Introduction In this post, we analyze a heat equation with rapidly oscillating coefficients dependent on a parameter , with a distributed control. We show that the uniform null controllability implies the uniform turnpike property, i.e., the turnpike property with constants independent of […]
Nonlinear hyperbolic systems: Modeling, controllabiliy and applications The control theory of hyperbolic systems is an important topic in continuum and fluid mechanics. Networks of nonlinear hyperbolic systems arise in real world applications, e.g. planar or out-of-plane networks of vibrating strings, shearable beams, gas networks and shallow […]
Kinetic theory of Bose Einstein Condensates If a dilute gas of bosons, about one-hundred-thousandth the density of normal air, is cooled to a temperature very close to absolute zero (0 K or -273.15C), the gas will be changed into a new state of matter, called Bose-Einstein […]
Transition Layers in Elliptic Equations By Maicon Sônego   Stable transition layers in an unbalanced bistable equation Consider the following semi-linear problem where are positive functions in ; is a positive parameter and We assume that the functions satisfy ; for all ; there is a […]
Randomized time-splitting in linear-quadratic optimal control By Daniël Veldman   Introduction Solving an optimal control problem for a large-scale dynamical system can be computationally demanding. This problem appears in numerous applications. One example is Model Predictive Control (MPC), which requires the solution of several optimal control […]

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