Optimal Control of Nonlinear Systems Using the Shifted Legendre Polynomials

  • Rahman Hajmohammadi Department of Electrical Engineering , Shahid Bahonar University of Kerman
  • Mohammad Ali Vali Department of Mathematics , Shahid Bahonar University of Kerman , Kerman
  • Mahmoud Samavat Department of Electrical Engineering , Shahid Bahonar University of Kerman
Keywords: Non-linear systems, Legendre Polynomials, Optimal Control, Numerical Methods


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.


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How to Cite
Hajmohammadi, R., Vali, M. A., & Samavat, M. (2014). Optimal Control of Nonlinear Systems Using the Shifted Legendre Polynomials. Majlesi Journal of Electrical Engineering, 8(2). Retrieved from http://mjee.iaumajlesi.ac.ir/index/index.php/ee/article/view/1167