TITLE:
Legendre Approximation for Solving a Class of Nonlinear Optimal Control Problems
AUTHORS:
Emran Tohidi, Omid Reza Navid Samadi, Mohammad Hadi Farahi
KEYWORDS:
Optimal Control, Legendre Polynomials, Linear Combination Property of Intervals, Chebyshev-Gauss-Lobatto Points, Nonlinear Programming
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.1 No.1,
June
1,
2011
ABSTRACT: This paper introduces a numerical technique for solving a class of optimal control problems containing nonlinear dynamical system and functional of state variables. This numerical method consists of two major parts. In the first part, using linear combination property of intervals, we convert the nonlinear dynamical system into an equivalent linear system. And in the second part, which we are dealing with a linear dynamical system, using Legendre expansions for approximating both the state and associated control together with discretizing the constraints over the Chebyshev-Gauss-Lobatto points, the optimal control problem is transformed into a corresponding NLP problem which is diretly solved. The proposed idea is illustrated by several numerical examples.