相关论文: Shape Optimization of Actuators over Banach Spaces…

Anisotropic fluids, such as nematic liquid crystals, can form non-spherical equilibrium shapes known as tactoids. Predicting the shape of these structures as a function of material parameters is challenging and paradigmatic of a broader…

We investigate optimal control of dynamical systems which are affine, i.e., linear in control, but nonlinear in state. The control task is to enforce the system state to follow a prescribed desired trajectory as closely as possible, a task…

In this article, we consider parabolic equations on a bounded open connected subset $\Omega$ of $\R^n$. We model and investigate the problem of optimal shape and location of the observation domain having a prescribed measure. This problem…

Motivated by some recent twaddles on Mazur rotations problem, we study the "dynamics" of the semigroup of contractive automorphisms of Banach spaces, mostly in finite-dimensional spaces. We focus on the metric aspects of the "action" of…

In this paper, we are concerned with the approximate controllability results for a class of impulsive functional differential control systems involving time dependent operators in Banach spaces. First, we show the existence of a mild…

This work is concerned with an optimal control problem governed by a non-smooth quasilinear elliptic equation with a nonlinear coefficient in the principal part that is locally Lipschitz continuous and directionally but not G\^ateaux…

In this article, a previously published amplifier-less potentiostat architecture is further examined. Starting with a linearized model, the impact of the most important parameters is studied taking in account the electrodes-solution…

This paper considers two different problems in trajectory tracking control for linear systems. First, if the control is not unique which is most input energy efficient. Second, if exact tracking is infeasible which control performs most…

We study a systematic way to produce a Lipschitz operator ideal from a Banach linear operator ideal $\mathcal A$. For maximal and minimal operator ideals $\mathcal A$, the Lipschitz maximal hull and minimal kernel of the Lipschitz operator…

In the nonlinear geometry of Banach spaces where the objects in the category are Banach spaces as in the linear case, the morphisms in the new setting are taken to comprise of certain nonlinear maps involving say, Lipschitz maps and, in…

This paper presents, using dynamical system theory, a framework for investigating the turnpike property in nonlinear optimal control. First, it is shown that a turnpike-like property appears in general dynamical systems with hyperbolic…

When solving a PDE problem numerically, a certain mesh-refinement process is always implicit, and very classically, mesh adaptivity is a very effective means to accelerate grid convergence. Similarly, when optimizing a shape by means of an…

In this work we present the first systematic framework to sculpt active nematics systems, using optimal control theory and a hydrodynamic model of active nematics. We demonstrate the use of two different control fields, (1) applied…

In this paper we discuss the optimal control of a quasilinear parabolic state equation. Its form is leaned on the kind of problems arising for example when controlling the anisotropic Allen-Cahn equation as a model for crystal growth.…

We present a new proof of the turnpike property for nonlinear optimal control problems, when the running target is a steady control-state pair of the underlying system. Our strategy combines the construction of quasi-turnpike controls via…

We optimize a selection of eigenvalues of the Laplace operator with Dirichlet or Neumann boundary conditions by adjusting the shape of the domain on which the eigenvalue problem is considered. Here, a phase-field function is used to…

We investigate a shape optimization problem for a heat-conducting fluid governed by a Boussinesq system. The main goal is to determine an optimal domain shape that yields a temperature distribution as uniform as possible. Initially, we…

This thesis deals with shape optimization for contact mechanics. More specifically, the linear elasticity model is considered under the small deformations hypothesis, and the elastic body is assumed to be in contact (sliding or with Tresca…

This article is devoted to the shape optimization of the internal structure of an electric motor, and more precisely of the arrangement of air and ferromagnetic material inside the rotor part with the aim to increase the torque of the…

We construct an optimally local perfect lattice action for free scalars of arbitrary mass, and truncate its couplings to a unit hypercube. Spectral and thermodynamic properties of this ``hypercube scalar'' are drastically improved compared…