Optimal Control of Nonlinear Systems Using the Shifted Legendre Polynomials

Majlesi Journal of Electrical Engineering

مقاله 4، دوره 8، شماره 2، مرداد 2014   

نوع مقاله: Review Article

نویسندگان

Rahman Hajmohammadi^{* 1}؛ Mohammad Ali Vali²؛ Mahmoud Samavat¹

¹Department of Electrical Engineering , Shahid Bahonar University of Kerman

²Department of Mathematics , Shahid Bahonar University of Kerman , Kerman

چکیده

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.

کلیدواژه‌ها

non-linear systems؛ en؛ legendre polynomials؛ Optimal Control؛ Numerical Methods

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