Ascent trajectory optimisation for hypersonic vehicles via Gauss pseudospectral method

Abstract

The objective of this paper is to investigate a reliable method to generate optimal ascent trajectory for hypersonic vehicles. When solving optimal trajectories in endo-atmospheric flight, most of traditional indirect methods suffer from difficulties in finding an appropriate initial guess and getting a convergent solution for two point boundary value problem (TPBVP). With improvements on on-board computer performance, direct methods such as pseudospectral method show promising potential for real-time optimal guidance. It removes the need for computing analytical gradients of aerodynamic coefficients, and remains high accurate solution similar to indirect methods. In this work, optimal ascent trajectory generation problem is formulated as a fuel-optimal control problem. Gauss pseudospectral method (GPM) is presented to generate the optimal ascent trajectories. Optimal solutions from GPM are compared with an indirect method based on finite difference method (FDM). Numerical simulations are studied with various initial conditions to investigate the optimal trajectory characteristics for hypersonic vehicles. The results verify the validity of GPM for ascent trajectory optimisation in both vertical plane and three-dimensional space.