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

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.