Solving Ascent Trajectory Optimization Problems by Radua Pseudospectral Method

Ascent trajectory optimization problem of air-breathing hypersonic vehicles is a highly nonlinear and nonconvex problems. Most of the early works focus on the traditional indirect method, which needs to derive the complete first-order necessary conditions of the trajectory optimization problem. The derivation process is too complicated and error-prone. Additionally, indirect method has a high demand on the initial guess, and it needs to give the initial guess of covariant variables without physical significance. In this paper, we solve the ascent trajectory optimization problem directly using Radau Pseudospectral Method (RPM). Firstly, the complex three-dimensional ascent trajectory optimization problem is established in detail. Conmmon inequality path constraints including those on dynamic pressure and aerodynamic bending moment are taken into account. The performance index is given as maximizing the final mass considering minimizing the fuel consumption. Subsequently, the ascent trajectory optimization problem is transformed into a nonlinear programming problem (NLP) by RPM. Finally, the ascent trajectory optimization for Generic Hypersonic Aerodynamic Model Example (GHAME) is solved by RPM and the optimal results demonstrate the rapidity, effectiveness and high precision of RPM. The comparison between optimal trajectories with and without path constraints shows that path constraints increase fuel consumption.