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This study is concerned with the numerical solution of a class ofinfinite-horizon linear regulation problems with state equality constraints andoutput feedback control. We propose two numerical methods to convert theoptimal control problem into nonlinear programming problems (NLPs) usingcollocations in a semi-infinite domain based on rational Gegenbauer (RG) andexponential Gegenbauer (EG) basis functions. We introduce new properties ofthese basis functions and derive their quadratures and associated truncationerrors. A rigorous stability analysis of the RG and EG interpolations is alsopresented. The effects of various parameters on the accuracy and efficiency ofthe proposed methods are investigated. The performance of the developedintegral spectral method is demonstrated using two benchmark test problemsrelated to a simple model of a divert control system and the lateral dynamicsof an F-16 aircraft. Comparisons of the results of the current study withavailable numerical solutions show that the developed numerical scheme isefficient and exhibits faster convergence rates and higher accuracy.

Direct Integral Pseudospectral and Integral Spectral Methods for Solving  a Class of Infinite Horizon Optimal Output Feedback Control Problems Using  Rational and Exponential Gegenbauer Polynomials