The Turnpike Solutions in the Quantum Systems Control Problem

10.12737/2413 ◽  
2013 ◽  
Vol 4 (4) ◽  
pp. 91-106 ◽  
Author(s):  
Ирина Гусева ◽  
Irina Guseva ◽  
Владимир Гурман ◽  
Vladimir Gurman ◽  
Олесь Фесько ◽  
...  
Keyword(s):  
Control Problem ◽  
Iterative Methods ◽  
Spin Chain ◽  
Optimization Problem ◽  
Quantum Systems ◽  
Computational Experiments ◽  
Degenerate Problems ◽  
Nonlinear Controls ◽  
Linear And Nonlinear ◽  
Systems Control

The optimization problem in a spin chain on the basis of Shr¨odinger equation is considered. The hamiltonian of the equation contains a combination of linear and nonlinear controls. Using the the degenerate problems theory, the problem is reduced to a regular derived problem. This transformation essentially increases the effectiveness of its investigation by iterative methods. The procedure is demonstrated in computational experiments with the use of visual example.

Non-integrability of the optimal control problem for n-level quantum systems

2017 ◽  
Vol 50 (17) ◽  
pp. 175202 ◽  
Author(s):  
Guillaume Duval ◽  
Andrzej Maciejewski ◽  
Witold Respondek
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Quantum Systems ◽  
N Level

scholarly journals Multigrid Method for Optimal Control Problem Constrained by Stochastic Stokes Equations with Noise

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 738
Author(s):  
Muhammad Munir Butt
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Line Search ◽  
Optimization Problem ◽  
Search Strategy ◽  
Stokes Equations ◽  
Applied Mathematics ◽  
Staggered Grid ◽  
Important Field ◽  
Three Factor

Optimal control problems governed by stochastic partial differential equations have become an important field in applied mathematics. In this article, we investigate one such important optimization problem, that is, the stochastic Stokes control problem with forcing term perturbed by noise. A multigrid scheme with three-factor coarsening to solve the corresponding discretized control problem is presented. On staggered grids, a three-factor coarsening strategy helps in simplifying the inter-grid transfer operators and reduction in computation (CPU time). For smoothing, a distributive Gauss–Seidel scheme with a line search strategy is employed. To validate the proposed multigrid staggered grid framework, numerical results are presented with white noise at the end.

scholarly journals Transport in one-dimensional integrable quantum systems

2020 ◽  
Author(s):  
Jesko Sirker
Keyword(s):  
Transport Properties ◽  
Spin Chain ◽  
Linear Response ◽  
Summer School ◽  
Condensed Matter ◽  
Quantum Systems ◽  
Integrable Models ◽  
One Dimensional ◽  
Integrable Quantum ◽  
Linear Response Regime

These notes are based on a series of three lectures given at the Les Houches summer school on ’Integrability in Atomic and Condensed Matter Physics’ in August 2018. They provide an introduction into the unusual transport properties of integrable models in the linear response regime focussing, in particular, on the spin-1/21/2 XXZ spin chain.

scholarly journals Robust Tracking Control of Mobile Robot Formation with Obstacle Avoidance

2007 ◽  
Vol 2007 ◽  
pp. 1-10 ◽  
Author(s):  
Tiantian Yang ◽  
Zhiyuan Liu ◽  
Hong Chen ◽  
Run Pei
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Formation Control ◽  
Optimization Problem ◽  
Reference Trajectory ◽  
Robust Tracking Control ◽  
Wheeled Mobile Robots ◽  
Lmi Optimization ◽  
Control Scheme

We consider the formation control problem of multiple wheeled mobile robots with parametric uncertainties and actuator saturations in the environment with obstacles. First, a nonconvex optimization problem is introduced to generate the collision-free trajectory. If the robots tracking along the reference trajectory find themselves moving close to the obstacles, a new collision-free trajectory is generated automatically by solving the optimization problem. Then, a distributed control scheme is proposed to keep the robots tracking the reference trajectory. For each interacting robot, optimal control problem is generated. And in the framework of LMI optimization, a distributed moving horizon control scheme is formulated as online solving each optimal control problem at each sampling time. Moreover, closed-loop properties inclusive of stability andH∞performance are discussed. Finally, simulation is performed to highlight the effectiveness of the proposed control law.

scholarly journals Nonlinear Inertia Weighted Teaching-Learning-Based Optimization for Solving Global Optimization Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Zong-Sheng Wu ◽  
Wei-Ping Fu ◽  
Ru Xue
Keyword(s):  
Global Optimization ◽  
Optimization Problem ◽  
Random Number ◽  
Nonlinear Problems ◽  
Tlbo Algorithm ◽  
Teaching Learning Based Optimization ◽  
Linear And Nonlinear ◽  
Weighted Factor ◽  
Teaching Learning ◽  
Dynamic Inertia

Teaching-learning-based optimization (TLBO) algorithm is proposed in recent years that simulates the teaching-learning phenomenon of a classroom to effectively solve global optimization of multidimensional, linear, and nonlinear problems over continuous spaces. In this paper, an improved teaching-learning-based optimization algorithm is presented, which is called nonlinear inertia weighted teaching-learning-based optimization (NIWTLBO) algorithm. This algorithm introduces a nonlinear inertia weighted factor into the basic TLBO to control the memory rate of learners and uses a dynamic inertia weighted factor to replace the original random number in teacher phase and learner phase. The proposed algorithm is tested on a number of benchmark functions, and its performance comparisons are provided against the basic TLBO and some other well-known optimization algorithms. The experiment results show that the proposed algorithm has a faster convergence rate and better performance than the basic TLBO and some other algorithms as well.

scholarly journals Multitarget Linear-Quadratic Control Problem: Semi-Infinite Interval

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
L. Faybusovich ◽  
T. Mouktonglang
Keyword(s):  
Convex Optimization ◽  
Control Problem ◽  
Optimization Problem ◽  
Infinite Interval ◽  
Linear Quadratic Control ◽  
Linear Quadratic ◽  
Convex Optimization Problem ◽  
Simple Convex ◽  
Linear Quadratic Control Problem

We consider multitarget linear-quadratic control problem on semi-infinite interval. We show that the problem can be reduced to a simple convex optimization problem on the simplex.

Linear and nonlinear liftings of states of quantum systems

2012 ◽  
Vol 19 (4) ◽  
pp. 417-427 ◽  
Author(s):  
G. G. Amosov ◽  
V. Zh. Sakbaev ◽  
O. G. Smolyanov
Keyword(s):  
Quantum Systems ◽  
Linear And Nonlinear

scholarly journals Shift-invert diagonalization of large many-body localizing spin chains

2018 ◽  
Vol 5 (5) ◽  
Author(s):  
Francesca Pietracaprina ◽  
Nicolas Macé ◽  
David J. Luitz ◽  
Fabien Alet
Keyword(s):  
Random Field ◽  
Linear Algebra ◽  
Spin Chain ◽  
Quantum Systems ◽  
Exact Diagonalization ◽  
Spin Chains ◽  
Many Body ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain ◽  
Sparse Linear Algebra

We provide a pedagogical review on the calculation of highly excited eigenstates of disordered interacting quantum systems which can undergo a many-body localization (MBL) transition, using shift-invert exact diagonalization. We also provide an example code at https://bitbucket.org/dluitz/sinvert_mbl. Through a detailed analysis of the simulational parameters of the random field Heisenberg spin chain, we provide a practical guide on how to perform efficient computations. We present data for mid-spectrum eigenstates of spin chains of sizes up to L=26L=26. This work is also geared towards readers with interest in efficiency of parallel sparse linear algebra techniques that will find a challenging application in the MBL problem.

Sign in / Sign up

Export Citation Format

Share Document