Chapter 7: Bang-Bang Control Problem and Its Induced Optimization Problem

2012 ◽  
pp. 299-338
Keyword(s):  
Control Problem ◽  
Optimization Problem ◽  
Bang Bang Control

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 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.

On Bene?' bang-bang control problem

1982 ◽  
Vol 9 (1) ◽  
pp. 163-176 ◽  
Author(s):  
N. Christopeit ◽  
K. Helmes
Keyword(s):  
Control Problem ◽  
Bang Bang Control

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.

Fuzzy Bang-Bang control problem under granular differentiability

2018 ◽  
Vol 355 (12) ◽  
pp. 4931-4951 ◽  
Author(s):  
Mehran Mazandarani ◽  
Yi Zhao
Keyword(s):  
Control Problem ◽  
Bang Bang Control

scholarly journals Mining Optimal Policies: A Pattern Recognition Approach to Model Analysis

2020 ◽  
Vol 2 (3) ◽  
pp. 145-166 ◽  
Author(s):  
Fernanda Bravo ◽  
Yaron Shaposhnik
Keyword(s):  
Machine Learning ◽  
Pattern Recognition ◽  
Control Problem ◽  
Admission Control ◽  
Optimization Problem ◽  
Numerical Solutions ◽  
Model Analysis ◽  
Optimal Policies ◽  
Complex Optimization ◽  
Pattern Recognition Approach

This project spawned from an admission control problem we were working on for a major hospital in the Boston area. We tried to incorporate various aspects of the problem in a model, which resulted in a complex optimization problem that was difficult to solve analytically. Although numerical solutions could be computed, we were looking for insights to characterize simple policies that could be used in practice. We then came up with the idea of using machine learning to analyze solutions as a mean for obtaining such insights, an idea we thought could be interesting by itself. The motivating problem is an ongoing separate work.

The least-time optimization for abnormity control of a complex industrial process

2018 ◽  
Vol 41 (5) ◽  
pp. 1468-1476
Author(s):  
Hui Li ◽  
Fuli Wang ◽  
Hongru Li ◽  
Xu Wang
Keyword(s):  
Control Problem ◽  
Control Strategy ◽  
Optimization Problem ◽  
External Environment ◽  
Industrial Process ◽  
Economic Loss ◽  
Industrial Processes ◽  
Mechanical Constraints ◽  
Time Optimization ◽  
Simulation Results

Modern complex industrial processes are prone to errors because of interactions between humans, the external environment and the equipment. When the abnormity degree of a system increases, the system can generate failures or even accidents, which result in serious economic loss or even personal casualties. Therefore, it is necessary to take effective measures to remove the abnormity as soon as possible. This problem can be described as the least-time optimization problem. This paper analyses an abnormity by summarizing and comparing related concepts in the researched results. Based on these concepts, a control strategy for the abnormity in a complex industrial process is proposed by analysing the experience of operators on site. Taking the abnormity in the thickening process of gold hydrometallurgy as an example, this paper explores how the abnormity control problem can be transformed into the least-time optimization problem. Technical and mechanical constraints are described. Simulation results indicate that the proposed strategy can assist the operators to regulate the control variables and recover the abnormity as soon as possible. This produces better performance than the existing regulations on site.

scholarly journals An SQP trust region method for solving the discrete-time linear quadratic control problem

2012 ◽  
Vol 22 (2) ◽  
pp. 353-363 ◽  
Author(s):  
El-Sayed Mostafa
Keyword(s):  
Control Problem ◽  
Discrete Time ◽  
Optimization Problem ◽  
Trust Region Method ◽  
Trust Region ◽  
Linear Quadratic Control ◽  
Linear Quadratic ◽  
Region Method ◽  
Time Linear ◽  
Linear Quadratic Control Problem

An SQP trust region method for solving the discrete-time linear quadratic control problemIn this paper, a sequential quadratic programming method combined with a trust region globalization strategy is analyzed and studied for solving a certain nonlinear constrained optimization problem with matrix variables. The optimization problem is derived from the infinite-horizon linear quadratic control problem for discrete-time systems when a complete set of state variables is not available. Moreover, a parametrization approach is introduced that does not require starting a feasible solution to initiate the proposed SQP trust region method. To demonstrate the effectiveness of the method, some numerical results are presented in detail.

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