scholarly journals Feedback Control Method Using Haar Wavelet Operational Matrices for Solving Optimal Control Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Waleeda Swaidan ◽  
Amran Hussin
Keyword(s):  
Optimal Control ◽  
Feedback Control ◽  
Optimal Control Problems ◽  
Control Method ◽  
Numerical Technique ◽  
Direct Methods ◽  
Haar Wavelet ◽  
Control Problems ◽  
Operational Matrices ◽  
Feedback Control Method

Most of the direct methods solve optimal control problems with nonlinear programming solver. In this paper we propose a novel feedback control method for solving for solving affine control system, with quadratic cost functional, which makes use of only linear systems. This method is a numerical technique, which is based on the combination of Haar wavelet collocation method and successive Generalized Hamilton-Jacobi-Bellman equation. We formulate some new Haar wavelet operational matrices in order to manipulate Haar wavelet series. The proposed method has been applied to solve linear and nonlinear optimal control problems with infinite time horizon. The simulation results indicate that the accuracy of the control and cost can be improved by increasing the wavelet resolution.

Numerical solution of time-delay optimal control problems by the operational matrix based on Hartley series

2021 ◽  
pp. 014233122110533
Author(s):  
Mahmood Dadkhah ◽  
Kamal Mamehrashi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Numerical Technique ◽  
Operational Matrix ◽  
Main Idea ◽  
Control Problems ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
The Cost ◽  
And Control

In this paper, a numerical technique based on the Hartley series for solving a class of time-delayed optimal control problems (TDOCPs) is introduced. The main idea is converting such TDOCPs into a system of algebraic equations. Thus, we first expand the state and control variables in terms of the Hartley series with undetermined coefficients. The delay terms in the problem under consideration are expanded in terms of the Hartley series. Applying the operational matrices of the Hartley series including integration, differentiation, dual, product, delay, and substituting the estimated functions into the cost function, the given TDOCP is reduced to a system of algebraic equations to be solved. The convergence of the proposed method is extensively investigated. At last, the precision and applicability of the proposed method is studied through different types of numerical examples.

An Indirect Method for Solving Non-Linear Optimal Control Problems in Power Systems-Part 2

1974 ◽  
Vol 11 (4) ◽  
pp. 313-321 ◽  
Author(s):  
O. P. Malik ◽  
B. K. Mukhopadhyay ◽  
P. Subramaniam
Keyword(s):  
Optimal Control ◽  
Power Systems ◽  
Optimal Control Problems ◽  
Numerical Technique ◽  
Continuation Method ◽  
Hybrid Approach ◽  
Control Problems ◽  
Linear Optimal Control ◽  
Non Linear ◽  
Linear Optimal Control Problems

This paper describes the application of quasilinearization algorithm and its various modifications to solve the non-linear optimal control problems in power systems. Results obtained by this indirect numerical technique are compared to those obtained by other, direct methods. It is shown that a proposed hybrid approach, in conjunction with the continuation method, can be considered as an effective iterative procedure for most practical problems in power systems.

Research on a collocation approach and three metaheuristic techniques based on MVO, MFO, and WOA for optimal control of fractional differential equation

2021 ◽  
pp. 107754632110514
Author(s):  
Asiyeh Ebrahimzadeh ◽  
Raheleh Khanduzi ◽  
Samaneh P A Beik ◽  
Dumitru Baleanu
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Focal Point ◽  
Control Problems ◽  
Operational Matrices ◽  
State Variables ◽  
Caputo Fractional Derivatives ◽  
Fractional Optimal Control ◽  
Whale Optimization ◽  
Fractional Optimal Control Problems

Exploiting a comprehensive mathematical model for a class of systems governed by fractional optimal control problems is the significant focal point of the current paper. The efficiency index is a function of both control and state variables and the dynamic control system relies on Caputo fractional derivatives. The attributes of Bernoulli polynomials and their operational matrices of fractional Riemann–Liouville integrations are applied to convert the optimization problem to the nonlinear programing problem. Executing multi-verse optimizer, moth-flame optimization, and whale optimization algorithm terminate to the most excellent solution of fractional optimal control problems. A study on the advantage and performance between these approaches is analyzed by some examples. Comprehensive analysis ascertains that moth-flame optimization significantly solves the example. Furthermore, the privilege and advantage of preference with its accuracy are numerically indicated. Finally, results demonstrate that the objective function value gained by moth-flame optimization in comparison with other algorithms effectively decreased.

SOLVING INFINITE-HORIZON OPTIMAL CONTROL PROBLEMS USING THE HAAR WAVELET COLLOCATION METHOD

2014 ◽  
Vol 56 (2) ◽  
pp. 179-191 ◽  
Author(s):  
ALIREZA NAZEMI ◽  
NEDA MAHMOUDY
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Direct Method ◽  
Infinite Horizon ◽  
Main Idea ◽  
Local Property ◽  
Haar Wavelet ◽  
Haar Wavelets ◽  
Control Problems ◽  
Wavelet Collocation Method

AbstractWe consider infinite-horizon optimal control problems. The main idea is to convert the problem into an equivalent finite-horizon nonlinear optimal control problem. The resulting problem is then solved by means of a direct method using Haar wavelets. A local property of Haar wavelets is applied to simplify the calculation process. The accuracy of the present method is demonstrated by two illustrative examples.

An Indirect Method for Solving Non-Linear Optimal Control Problems in Power Systems-Part 1

1974 ◽  
Vol 11 (3) ◽  
pp. 273-282
Author(s):  
O. P. Malik ◽  
B. K. Mukhopadhyay ◽  
P. Subramaniam
Keyword(s):  
Optimal Control ◽  
Power Systems ◽  
Optimal Control Problems ◽  
Numerical Technique ◽  
Continuation Method ◽  
Hybrid Approach ◽  
Control Problems ◽  
Linear Optimal Control ◽  
Non Linear ◽  
Linear Optimal Control Problems

This paper describes the application of quasilinearization algorithm and its various modifications to solve the non-linear optimal control problems in power systems. Results obtained by this indirect numerical technique are compared to those obtained by other, direct methods. It is shown that a proposed hybrid approach, in conjunction with the continuation method, can be considered as an effective iterative procedure for most practical problems in power systems.

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