Radial basis functions approach on optimal control problems: a numerical investigation

被引:10
|
作者
Rad, Jamal Amani [1 ]
Kazem, Saeed [2 ]
Parand, Kourosh [1 ]
机构
[1] Shahid Beheshti Univ, Fac Math Sci, Dept Comp Sci, Tehran 0098, Iran
[2] Amirkabir Univ Technol, Fac Math & Comp Sci, Dept Appl Math, Tehran, Iran
关键词
Optimal control problems; radial basis functions; collocation method; Gaussian RBF; Lagrange multipliers; CONTROLLED DUFFING OSCILLATOR; DATA APPROXIMATION SCHEME; DIFFERENTIAL-EQUATIONS; INTEGRAL-EQUATIONS; COLLOCATION METHOD; MESHLESS METHOD; SYSTEMS; MULTIQUADRICS; FORMULATION; ALGORITHM;
D O I
10.1177/1077546312472919
中图分类号
O42 [声学];
学科分类号
070206 ; 082403 ;
摘要
A numerical method for solving optimal control problems is presented in this work. The method is based on radial basis functions (RBFs) to approximate the solution of the optimal control problems by using collocation method. We applied Legendre-Gauss-Lobatto points for RBFs center nodes to use numerical integration method more easily, then the method of Lagrange multipliers is used to obtain the optimum of the problems. For this purpose different applications of RBFs are used. The differential and integral expressions which arise in the system dynamics, the performance index and the boundary conditions are converted into some algebraic equations which can be solved for the unknown coefficients. Illustrative examples are included to demonstrate the validity and applicability of the technique.
引用
收藏
页码:1394 / 1416
页数:23
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