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Modified Iterative Algorithm for Solving Optimal Control Problems
Current Issue
Volume 6, 2019
Issue 2 (June)
Pages: 20-27   |   Vol. 6, No. 2, June 2019   |   Follow on         
Paper in PDF Downloads: 19   Since Jul. 16, 2019 Views: 973   Since Jul. 16, 2019
Authors
[1]
Maha Delphi, Department of Applied Sciences, University of Technology, Baghdad, Iraq.
[2]
Suha Shihab, Department of Applied Sciences, University of Technology, Baghdad, Iraq.
Abstract
In this paper, the study of problems in optimal control is very important in our day life and their applications can be studied in many disciplines based on mathematical modeling physics, chemistry and economy. Because of the complexity of most applications, optimal control problems are solved numerically. New techniques for achieving an approximate solution to optimal control problems are considered. They are based upon B-spline polynomials approximation with state parameterization method. New useful property of B-spline polynomials is first derived then, it is utilized to propose a modified restarted technique to reduce the number of unknown parameters with fast convergence. Furthermore, it can be proved that with special knot sequence, the B-spline basis are exactly Bernstein polynomials. The objective of the present work is to propose an approximate technique for solving linear and nonlinear optimal control problems is presented. The algorithm modifies previous works to certain optimal control problems and is depended on a Bernstein series expansion of state parameterization. The differential expressions from the constraint and the cost index as well as the boundary conditions are reduced into algebraic equations. The technique starts from initial trajectory is based on the boundary conditions then new iterative method with the help Bernstein polynomials and produces satisfactory convergence with small number of unknown parameters. The applicability of the proposed algorithm is illustrated on four linear and nonlinear optimal control problems. The comparison with other works is also included in this paper.
Keywords
Bernstein Polynomials (BEPs), Optimal Control Problems (OCPs), Parameterization Technique
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