Radial basis functions approach on optimal control problems: a numerical investigation. (July 2014)

• Record Type: Journal Article
• Authors: Rad, Jamal Amani; Kazem, Saeed; Parand, Kourosh
• Is Part Of: Journal of vibration and control. Volume 20:Number 9(2014)
• Page Start: 1394
• Page End: 1416
• Publication Date: 2014-07
• Subjects: Optimal control problems -- radial basis functions -- collocation method -- Gaussian RBF -- Lagrange multipliers; Vibration -- Periodicals; Damping (Mechanics) -- Periodicals; 620.3
• DOI: 10.1177/1077546312472919
• Languages: English
• ISSNs: 1077-5463

Abstract

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.