A composite Chebyshev finite difference method for nonlinear optimal control problems. (English) Zbl 1282.65075

Marzban, H. R.; Hoseini, S. M.

Commun. Nonlinear Sci. Numer. Simul. 18, No. 6, 1347-1361 (2013).

A composite Chebyshev finite difference method based on hybrid of block-pulse functions and Chebyshev polynomials using the Chebyshev-Gauss-Lobatto points is employed for solving nonlinear time-varying optimal control problems governed by ordinary differential equations. The efficiency of the globally convergent method is demonstrated through numerical examples governed by ordinary differential equations. The advantages of the proposed method are an easy implementation and a good representation of smooth and nonsmooth functions by finite hybrid expansion.

Reviewer: Bülent Karasözen (Ankara)

MSC:

65K10	Numerical optimization and variational techniques
49M25	Discrete approximations in optimal control
49J15	Existence theories for optimal control problems involving ordinary differential equations

Keywords:

nonlinear optimal control; composite Chebyshev finite differences; hybrid functions; Chebyshev-Gauss-Lobatto points; global convergence; numerical examples