Optimal Control of Nonlinear Systems Using the Shifted Legendre Polynomials

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  • Rahman Hajmohammadi1,
  • Mohammad Ali Vali2,
  • Mahmoud Samavat2,
  1. Department of Electrical Engineering , Shahid Bahonar University of Kerman
  2. Shahid Bahonar University of Kerman

Published in Issue 2024-02-21

How to Cite

Hajmohammadi, R., Vali, M. A., & Samavat, M. (2024). Optimal Control of Nonlinear Systems Using the Shifted Legendre Polynomials. Majlesi Journal of Electrical Engineering, 8(2). https://oiccpress.com/mjee/article/view/5275

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Abstract

A numerical technique based on Legendre Polynomials for finding optimal control of nonlinear systems with quadratic performance index is presented. An operational matrix of integration and product matrix are introduced and are used to reduce the nonlinear differential equations to the solution of nonlinear algebraic equations. The optimal solution of two classes of first and second order nonlinear systems is considered. In the case of second-order nonlinear systems, a new approach is introduced to find the optimal solution. In both cases, numerical examples are given and compared with the Taylor polynomial to confirm the accuracy of the proposed method.

Keywords

  • legendre polynomials,
  • Non-linear systems,
  • Numerical Methods.,
  • Optimal Control
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