M. Razzaghi and G. Elnagar, “A Legendre Technique For Solving Time-Varing Linear Quadratic Optimal Control Problems,” Journal of the Franklin Institute, Vol. 330, No. 3, 1993, pp. 453-463. doi:10.1016/0016-0032(93)90092-9

has been cited by the following article:

• 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.