Direct Method of solving optimal control problems

2014 ◽  
Vol 40 ◽  
pp. 123-134
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Direct Method ◽  
Control Problems

Orthonormal piecewise Bernoulli functions: Application for optimal control problems generated using fractional integro-differential equations

2022 ◽  
pp. 107754632110593
Author(s):  
Mohammad Hossein Heydari ◽  
Mohsen Razzaghi ◽  
Zakieh Avazzadeh
Keyword(s):  
Optimal Control ◽  
Fractional Integral ◽  
Original Problem ◽  
Optimal Control Problems ◽  
Integration Method ◽  
Direct Method ◽  
Fractional Integration ◽  
Basis Functions ◽  
Control Problems ◽  
Bernoulli Functions

In this study, the orthonormal piecewise Bernoulli functions are generated as a new kind of basis functions. An explicit matrix related to fractional integration of these functions is obtained. An efficient direct method is developed to solve a novel set of optimal control problems defined using a fractional integro-differential equation. The presented technique is based on the expressed basis functions and their fractional integral matrix together with the Gauss–Legendre integration method and the Lagrange multipliers algorithm. This approach converts the original problem into a mathematical programming one. Three examples are investigated numerically to verify the capability and reliability of the approach.

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.

Study of B-spline collocation method for solving fractional optimal control problems

2021 ◽  
pp. 014233122098753
Author(s):  
Yousef Edrisi-Tabriz ◽  
Mehrdad Lakestani ◽  
Mohsen Razzaghi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Direct Method ◽  
Operational Matrix ◽  
Control Problems ◽  
Spline Collocation ◽  
B Spline ◽  
Fractional Optimal Control ◽  
Fractional Optimal Control Problems ◽  
A Direct Method

In this article, a class of fractional optimal control problems (FOCPs) are solved using a direct method. We present a new operational matrix of the fractional derivative in the sense of Caputo based on the B-spline functions. Then we reduce the solution of fractional optimal control problem to a nonlinear programming (NLP) one, where some existing well-developed algorithms may be applied. Numerical results demonstrate the efficiency of the presented technique.

scholarly journals Direct method for solution variational problems by using Hermite polynomials

2021 ◽  
Vol 39 (6) ◽  
pp. 223-237 ◽  
Author(s):  
Ayatollah Yari ◽  
Mirkamal Mirnia
Keyword(s):  
Optimal Control ◽  
Numerical Approximation ◽  
Optimal Control Problems ◽  
Direct Method ◽  
Hermite Polynomials ◽  
Variational Problems ◽  
Computational Method ◽  
Control Problems ◽  
Operational Matrices

‎In this approach‎, ‎one‎ computational method is presented for numerical approximation of variational problems‎. ‎This method with variable ‎coeffici‎ents is based on Hermite polynomials‎. ‎The properties of Hermite polynomials with the operational matrices of derivative and integration are used to reduce optimal control problems to the solution of linear algebraic equations‎. ‎Illustrative examples are included to demonstrate the validity and applicability of the technique‎.  

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