Authors | Sohrab Effati |
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Journal | Numerical Algebra, Control and Optimization |
Page number | 101-112 |
Serial number | 9 |
Volume number | 1 |
Paper Type | Full Paper |
Published At | 2019 |
Journal Grade | ISI |
Journal Type | Typographic |
Journal Country | Iran, Islamic Republic Of |
Journal Index | Scopus |
Abstract
In this paper, we derive the operational matrices of integration, derivative and production of Hermite wavelets and use a direct numerical method based on Hermite wavelet, for solving optimal control problems. The properties of Hermite polynomials are used for finding these matrices. First, we approximate the state and control variables by Hermite wavelets basis; then, the operational matrices is used to transfer the given problem into a linear system of algebraic equations. In fact, operational matrices of Hermite wavelet are employed to achieve a linear algebraic equation, in place of the dynamical system in terms of the unknown coefficients. The solution of this system gives us the solution of the original problem. Numerical examples with time varying and time invariant coefficient are given to demonstrate the applicability of these matrices.
tags: Optimal control problem, Hermite polynomial, Hermite wavelet, Operational matrix, Direct method