  This study is concerned with the numerical solution of a class of
infinite-horizon linear regulation problems with state equality constraints and
output feedback control. We propose two numerical methods to convert the
optimal control problem into nonlinear programming problems (NLPs) using
collocations in a semi-infinite domain based on rational Gegenbauer (RG) and
exponential Gegenbauer (EG) basis functions. We introduce new properties of
these basis functions and derive their quadratures and associated truncation
errors. A rigorous stability analysis of the RG and EG interpolations is also
presented. The effects of various parameters on the accuracy and efficiency of
the proposed methods are investigated. The performance of the developed
integral spectral method is demonstrated using two benchmark test problems
related to a simple model of a divert control system and the lateral dynamics
of an F-16 aircraft. Comparisons of the results of the current study with
available numerical solutions show that the developed numerical scheme is
efficient and exhibits faster convergence rates and higher accuracy.
