scholarly journals Numerical Methods for Solving Optimal Control Problem Using Scaling Boubaker Function

2020 ◽  
Vol 25 (2) ◽  
pp. 78-89 ◽  
Author(s):  
Eman Hassan Ouda Alfrdji ◽  
Imad Noah Ahmed
Keyword(s):  
Optimal Control ◽  
Numerical Methods ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Approximation Method ◽  
Numerical Examples ◽  
Control Parameterization ◽  
Matlab Program ◽  
And Control

      In this paper, the approximation method was used for solving optimal control problem (OCP), two techniques for state parameterization and control parameterization have been considered with the aid of Scaling Polynomials (SBP) represent a new important technique for solving (OCP’s). The algorithms were illustrated by several numerical examples using Matlab program. The results were evaluated and graphed to show the accuracy  of the methods.

scholarly journals Delayed Stochastic Linear-Quadratic Control Problem and Related Applications

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Li Chen ◽  
Zhen Wu ◽  
Zhiyong Yu
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Stochastic Differential Equations ◽  
Backward Stochastic Differential Equations ◽  
Delay System ◽  
Linear Quadratic ◽  
Stochastic Linear System ◽  
And Control

We discuss a quadratic criterion optimal control problem for stochastic linear system with delay in both state and control variables. This problem will lead to a kind of generalized forward-backward stochastic differential equations (FBSDEs) with Itô’s stochastic delay equations as forward equations and anticipated backward stochastic differential equations as backward equations. Especially, we present the optimal feedback regulator for the time delay system via a new type of Riccati equations and also apply to a population optimal control problem.

scholarly journals A global method for some class of optimization and control problems

2000 ◽  
Vol 23 (9) ◽  
pp. 605-616 ◽  
Author(s):  
R. Enkhbat
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Convex Function ◽  
Control Problem ◽  
Optimality Condition ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Global Method ◽  
Optimization And Control ◽  
And Control

The problem of maximizing a nonsmooth convex function over an arbitrary set is considered. Based on the optimality condition obtained by Strekalovsky in 1987 an algorithm for solving the problem is proposed. We show that the algorithm can be applied to the nonconvex optimal control problem as well. We illustrate the method by describing some computational experiments performed on a few nonconvex optimal control problems.

Optimal Design and Control of a Rotating Flexible Arm With ACLD Treatment

Aerospace ◽  
2003 ◽  
Author(s):  
E. H. K. Fung ◽  
D. T. W. Yau
Keyword(s):  
Optimal Control ◽  
Optimal Design ◽  
Shear Modulus ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Performance Index ◽  
Flexible Arm ◽  
Design Variables ◽  
And Control ◽  
Optimal Design And Control

In this paper, the optimal design and control of a rotating clamped-free flexible arm with fully covered active constrained layer damping (ACLD) treatment are studied. The arm is rotating in a horizontal plane in which the gravitational effect and rotary inertia are neglected. The piezo-sensor voltage is fed back to the piezo-actuator via a PD controller. Finite element method (FEM) in conjunction with Hamilton’s principle is used to derive the governing equations of motion of the system which takes into account the effects of centrifugal stiffening due to the rotation of the beam. The damping behavior of the viscoelastic material (VEM) is modeled using the complex shear modulus method. The design optimization objective is to maximize the sum of the first three open-loop modal damping ratios divided by the weight of the damping treatment. A genetic algorithm, differential evolution (DE), combined with a gradient-based algorithm, sequential quadratic programming (SQP), is used to determine the optimal design variables such as the thickness and storage shear modulus of the VEM core. Next for the determined optimal design variables, the optimal control problem is performed to determine the optimal control gains which minimize a quadratic performance index. The control performance index is normalized with respect to the initial conditions and the optimal control problem is posed to solve a min-max optimization problem. The results of this study will be useful in the optimal design and control of adaptive and smart rotating structures such as rotorcraft blades or robotic arms.

scholarly journals Optimal control theory with general constraints

1981 ◽  
Vol 23 (2) ◽  
pp. 115-126 ◽  
Author(s):  
John M. Blatt
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Control Theory ◽  
Time Dependent ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
General Constraints ◽  
Elementary Methods ◽  
And Control

AbstractWe consider an optimal control problem with, possibly time-dependent, constraints on state and control variables, jointly. Using only elementary methods, we derive a sufficient condition for optimality. Although phrased in terms reminiscent of the necessary condition of Pontryagin, the sufficient condition is logically independent, as can be shown by a simple example.

A morley finite element method for an elliptic distributed optimal control problem with pointwise state and control constraints

2018 ◽  
Vol 24 (3) ◽  
pp. 1181-1206 ◽  
Author(s):  
Susanne C. Brenner ◽  
Thirupathi Gudi ◽  
Kamana Porwal ◽  
Li-yeng Sung
Keyword(s):  
Finite Element Method ◽  
Optimal Control ◽  
Finite Element ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Constraints ◽  
Distributed Optimal Control ◽  
And Control ◽  
State And Control Constraints ◽  
Element Method

We design and analyze a Morley finite element method for an elliptic distributed optimal control problem with pointwise state and control constraints on convex polygonal domains. It is based on the formulation of the optimal control problem as a fourth order variational inequality. Numerical results that illustrate the performance of the method are also presented.

Ant Colony Optimization for Optimal Control in Manufacturing Engineering

2013 ◽  
Vol 340 ◽  
pp. 273-276
Author(s):  
Jie Bai ◽  
Li Zu ◽  
Wei Liu
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Ant Colony Optimization ◽  
Heuristic Algorithm ◽  
Numerical Results ◽  
Ant Colony ◽  
Control Input ◽  
Algorithm Optimization ◽  
And Control

A meta-heuristic algorithm optimization, Ant Colony Optimization, is used to solve a general optimal control problem. Ant Colony Optimization is introduced briefly in this paper. The disc resection of the control time and control input is investigated. A piece wise interval is considered in the converting. And the simulation in numerical results show this strategy is feasible and effective.

scholarly journals An Iterative Method for Solving Quadratic Optimal Control Problem Using Scaling Boubaker Polynomials

2020 ◽  
Vol 5 (2) ◽  
Author(s):  
Imad Noah Ahmed ◽  
Eman Hassan Ouda
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Iterative Method ◽  
Control Problem ◽  
Iteration Method ◽  
Numerical Examples ◽  
Boubaker Polynomials ◽  
Quadratic Optimal Control

  Abstract     In this paper, an iteration method was used for solving a quadratic optimal control problem (QOCP) by the aid of state parameterization technique and scaling Boubaker polynomials. Some numerical examples were added to show the applicability of the method, also a comparison with other method was presented. The process steps were illustrated by some numerical examples with graphs done by Matlab.

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