Multiple stage satellite launch vehicle ascent optimization using Chebyshev wavelets

Abstract

In this study, the problem of determining an optimal trajectory of a Multiple Stage Satellite Launch Vehicle (MSLV) was investigated using Chebyshev wavelets. The objective was to maneuver the MSLV from the ground to the target orbit while maximizing the remaining fuel in the upper stage. The method was based on Chebyshev wavelets approximation. This method consisted of reducing the optimal control problem to a system of algebraic equations by expanding the state rate and control vector as Chebyshev wavelets with undetermined coefficients. Firstly, the operational matrix of integration and the Gauss integration formula were employed to evaluate the performance index and the inequality constraints were converted into a set of algebraic equalities. Finally, these equalities were collocated at the Gauss nodes; thus, great simplifying problem solution was achieved. The suggested strategy is not complicated and can be implemented without too much fuss.