期刊名称：Journal of Interpolation and Approximation in Scientific Computing
印刷版ISSN：2194-3907
电子版ISSN：2194-3907
出版年度：2014
卷号：2014
DOI：10.5899/2014/jiasc-00033
出版社：ISPACS GmbH
摘要：In this paper, we present a computational method for solving optimal control problems and the controlled Duffing oscillator. This method is based on state parametrization. In fact, the state variable is approximated by Boubaker polynomials with unknown coefficients. The equation of motion, performance index and boundary conditions are converted into some algebraic equations. Thus, an optimal control problem converts to a optimization problem, which can then be solved easily. By this method, the numerical value of the performance index is obtained. Also, the control and state variables can be approximated as functions of time. Convergence of the algorithms is proved. Numerical results are given for several test examples to demonstrate the applicability and efficiency of the method.
关键词：Optimal control problems; Controlled linear and Duffing oscillator; Boubaker polynomials expansion scheme (BPES); optimization problem; Weierstrass approximation theorem
