scholarly journals Analytical solution of the optimal laser control problem in two-level systems

2004 ◽  
Vol 37 (12) ◽  
pp. 2569-2575 ◽  
Author(s):  
Martin E Garcia ◽  
Ilia Grigorenko
Keyword(s):  
Analytical Solution ◽  
Control Problem ◽  
Two Level Systems ◽  
Laser Control

scholarly journals Intrinsic Optimal Control for Mechanical Systems on Lie Group

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Chao Liu ◽  
Shengjing Tang ◽  
Jie Guo
Keyword(s):  
Optimal Control ◽  
Analytical Solution ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Lie Group ◽  
Control Method ◽  
Geodesic Distance ◽  
Infinite Horizon ◽  
Mechanical Systems ◽  
Programming Approach

The intrinsic infinite horizon optimal control problem of mechanical systems on Lie group is investigated. The geometric optimal control problem is built on the intrinsic coordinate-free model, which is provided with Levi-Civita connection. In order to obtain an analytical solution of the optimal problem in the geometric viewpoint, a simplified nominal system on Lie group with an extra feedback loop is presented. With geodesic distance and Riemann metric on Lie group integrated into the cost function, a dynamic programming approach is employed and an analytical solution of the optimal problem on Lie group is obtained via the Hamilton-Jacobi-Bellman equation. For a special case on SO(3), the intrinsic optimal control method is used for a quadrotor rotation control problem and simulation results are provided to show the control performance.

Optimal Dispensing Strategy for a Two Component Xerographic Development Process

2008 ◽  
Author(s):  
Feng Liu ◽  
George T.-C. Chiu ◽  
Eric S. Hamby ◽  
Yongsoon Eun
Keyword(s):  
Optimal Control ◽  
Analytical Solution ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Development Stage ◽  
Order System ◽  
Color Reproduction ◽  
Constrained Optimal Control ◽  
The Maximum Principle ◽  
Constrained Optimal Control Problem

Inconsistent color reproduction is a major performance and quality issue for high volume digital press. Literature has shown that loss of developability of the toner particles in the development stage of xerography is a main contributing factor for inconsistent color reproduction. Previous works have shown that a second order system model is able to predict and characterize the inevitable loss of developability. In this paper, a nonlinear constrained optimal control problem is formulated to find the optimal dispensing strategy that maximizes the time for which acceptable developability is maintained. An analytical solution to the constrained optimal control problem is derived based on the Maximum Principle without explicitly solving for the costate dynamics. Results show that the state feedback based optimal dispensing strategy starts with the minimal allowable dispensing rate while increasing the development voltage to maintain the desired development quality until the maximal development voltage is reached. Then, the optimal dispense rate switches to maintain the developability at maximal development voltage. Numerical examples support the analytical solution.

Finite element analysis of the constrained Dirichlet boundary control problem governed by the diffusion problem

2020 ◽  
Vol 26 ◽  
pp. 78
Author(s):  
Thirupathi Gudi ◽  
Ramesh Ch. Sau
Keyword(s):  
Finite Element ◽  
Control Problem ◽  
Dirichlet Boundary ◽  
A Priori ◽  
Diffusion Problem ◽  
Discrete Control ◽  
Optimal Order ◽  
Control Constraints ◽  
Element Analysis ◽  
Dirichlet Boundary Control

We study an energy space-based approach for the Dirichlet boundary optimal control problem governed by the Laplace equation with control constraints. The optimality system results in a simplified Signorini type problem for control which is coupled with boundary value problems for state and costate variables. We propose a finite element based numerical method using the linear Lagrange finite element spaces with discrete control constraints at the Lagrange nodes. The analysis is presented in a combination for both the gradient and the L2 cost functional. A priori error estimates of optimal order in the energy norm is derived up to the regularity of the solution for both the cases. Theoretical results are illustrated by some numerical experiments.

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