  This paper presents a Fourier integral pseudospectral (FIPS) method for a
general class of nonlinear, periodic optimal control (OC) problems with
equality and/or inequality constraints and sufficiently smooth solutions. In
this scheme, the integral form of the problem is collocated at an equispaced
set of nodes, and all necessary integrals are approximated using highly
accurate Fourier integration matrices (FIMs). The proposed method leads to a
nonlinear programming problem (NLP) with algebraic constraints, which is solved
using a direct numerical optimization method. Sharp convergence and error
estimates are derived for Fourier series, interpolants, and quadratures used
for smooth and continuous periodic functions. Two nonlinear examples are
considered to show the accuracy and efficiency of the numerical scheme.
