相关论文: Computing the optimal protocol for finite-time pro…
We derive optimal-work finite time protocols for a colloidal particle in a Gaussian well in the general non-Markovian underdamped regime in contact with a single reservoir. Optimal work protocols with and without measurements of position…
We consider Lagrangian systems in the limit of infinitely many particles. It is shown that the corresponding discrete action functionals Gamma-converge to a continuum action functional acting on probability measures of particle…
The analysis and boundary optimal control of the nonlinear transport of gas on a network of pipelines is considered. The evolution of the gas distribution on a given pipe is modeled by an isothermal semilinear compressible Euler system in…
The problem of finding an optimal curve for the target magnetic axis of a stellarator is addressed. Euler-Lagrange equations are derived for finite length three-dimensional curves that extremise their bending energy while yielding fixed…
This study introduces an approach to obtain a neighboring extremal optimal control (NEOC) solution for a closed-loop optimal control problem, applicable to a wide array of nonlinear systems and not necessarily quadratic performance indices.…
We will make a link between the steepest descent method for an unconstrained minimisation problem and fixed-point iterations for its Euler-Lagrange equation. In this context, we shall rediscover the preconditioned nonlinear conjugate…
The integrating factor technique is widely used to solve numerically (in particular) the Schr\"odinger equation in the context of spectral methods. Here, we present an improvement of this method exploiting the freedom provided by the gauge…
We present a Lagrange--Galerkin scheme free from numerical quadrature for the Navier--Stokes equations. Our idea is to use a locally linearized velocity and the backward Euler method in finding the position of fluid particle at the previous…
Micro- and nano-scale systems driven by rapid changes in control parameters (control protocols) dissipate significant energy. In the fast-protocol limit, we find that protocols that minimize dissipation at fixed duration are universally…
This paper is concerned with the large time behavior of solutions to the Euler-Fourier system with damping in $\mathbb{R}^{d}~(d\geq1)$. A time-weighted energy argument has been developed within the $L^2$ framework to derive the optimal…
A continuous optimal control problem governed by an elliptic variational inequality was considered in Boukrouche-Tarzia, Comput. Optim. Appl., 53 (2012), 375-392 where the control variable is the internal energy $g$. It was proved the…
In this paper, we consider an optimal control problem in equilibrium thermodynamics of gases. Thermodynamic state of the gas is given by a Legendrian submanifold in a contact thermodynamic space. Using Pontryagin's maximum principle we find…
We study the thermodynamic cost associated with the erasure of one bit of information over a finite amount of time. We present a general framework for minimizing the average work required when full control of a system's microstates is…
We consider nonsmooth optimal control problems subject to a linear elliptic partial differential equation with homogeneous Dirichlet boundary conditions. It is well-known that local solutions satisfy the celebrated Pontryagin maximum…
We present an optimal control procedure for the non-adiabatic transport of ultracold neutral thermal atoms in optical tweezers arranged in a one-dimensional array, with focus on reaching minimal transfer time. The particle dynamics are…
For quantum computers to become useful tools to physicists, engineers and computational scientists, quantum algorithms for solving nonlinear differential equations need to be developed. Despite recent advances, the quest for a solver that…
In this paper, we study numerical approximations for optimal control of a class of stochastic partial differential equations with partial observations. The system state evolves in a Hilbert space, whereas observations are given in…
Euler's elastica model has been extensively studied and applied to image processing tasks. However, due to the high nonlinearity and nonconvexity of the involved curvature term, conventional algorithms suffer from slow convergence and high…
We analyze the control of the motion of a charged particle by means of an external electric field. The system is constrained to move along a given direction. The goal of the control is to change the speed of the particle in a fixed time…
In this work, we study the nonequilibrium statistical properties of the relaxation dynamics of a nanoparticle trapped in a harmonic potential. We report an exact time-dependent analytical solution to the Langevin dynamics that arises from…