Comments on "Optimal control via Fourier series of operational matrix of integration"

In the last four decades, the orthogonal functions approach has been extensively applied to study problems like analysis, identification, and control of continuous-time dynamical systems. The success of this approach lies in the fact that it converts calculus into algebra approximately in the sense of least squares. Sine-cosine functions are a class of orthogonal functions, and they were applied to study the optimal control problem with some success. In order to have a computationally attractive method for solving the optimal control problem via sine-cosine functions, an attempt was made. In this note, we show that the Fourier series approach to the optimal control problem in a paper by Endow (Optimal control via Fourier series of operational matrix of integration, IEEE Trans. Autom. Control, vol. 34, no. 7, p. 770-3, Jul. 1989) is incorrect.