Abass, G.; Shihab, S. Operational Matrix of New Shifted Wavelet Functions for Solving Optimal Control Problem. Mathematics2023, 11, 3040.
Abass, G.; Shihab, S. Operational Matrix of New Shifted Wavelet Functions for Solving Optimal Control Problem. Mathematics 2023, 11, 3040.
Abass, G.; Shihab, S. Operational Matrix of New Shifted Wavelet Functions for Solving Optimal Control Problem. Mathematics2023, 11, 3040.
Abass, G.; Shihab, S. Operational Matrix of New Shifted Wavelet Functions for Solving Optimal Control Problem. Mathematics 2023, 11, 3040.
Abstract
The present work concerns with presenting an explicit formula for new shifted wavelet (NSW) functions. Wavelet functions have many applications and advantages in both applied and theoretical fields. They are formulated with different orthogonal polynomials to construct new techniques for treating some problems in sciences, and engineering. A new important differentiation property of NSW in terms of NSW themselves is obtained and proved in this paper. Then it is utilized together with the state parameterization technique to find solution of optimal control problem (OCP) approximately. The suggested method converts the OCP into a quadratic programming problem, which can be easily determined on computer. As a result, the approximate solution closes with the exact solution even with a small number of NSW utilized in estimation. The error bound estimation for the proposed method is also discussed. Some test numerical examples are solved to demonstrate the applicability of the suggested method. For comparison, the exact known solutions against the obtained approximate results are listed in Tables.
Keywords
New shifted wavelet functions; optimal control problem; Convergence criteria; Error analysis
Subject
Computer Science and Mathematics, Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
