The Sine-Cosine Wavelet and Its Application in the Optimal Control of Nonlinear Systems with Constraint

Abstract

In this paper, an optimal control of quadratic performance index with nonlinear constrained is presented. The sine-cosine wavelet operational matrix of integration and product matrix are introduced and applied to reduce nonlinear differential equations to the nonlinear algebraic equations. Then, the Newton-Raphson method is used for solving these sets of algebraic equations. To present ability of the proposed method, two classes, first order system and second order system, are considered. The obtained results show that the proposed method offers improved performance. In this paper, an optimal control of quadratic performance index with nonlinear constrained is presented. The sine-cosine wavelet operational matrix of integration and product matrix are introduced and applied to reduce nonlinear differential equations to the nonlinear algebraic equations. Then, the Newton-Raphson method is used for solving these sets of algebraic equations. To present ability of the proposed method, two classes, first order system and second order system, are considered. The obtained results show that the proposed method offers improved performance