Abstract: This paper proposes a trajectory optimization approach for the real-time atmospheric ascent trajectory optimization problem based on Proximal-Newton-Kantorovich convex programming. The Newton-Kantorovich iteration approach casts the trajectory optimization problem into subproblems with each being a linear optimal control problem. However, the Newton-Kantorovich iteration approach ignores higher order terms in motion equations, making it hard to converge. This paper proposes a Proximal-Newton-Kantorovich iteration approach. A Proximal term is introduced in the performance index of the subproblems to improve the convergence. The subproblems are then casted into second-order cone programming problems and solved by the interior-point methods. The proposed Proximal-Newton-Kantorovich iteration approach is an efficient approach to solve nonlinear trajectory optimization problems. It is proved that the convergence results of the Proximal-Newton-Kantorovich iteration approach always satisfy the necessary conditions of the original trajectory optimization problem. Numerical results show that this approach can be executed in milliseconds.

Key words: hypersonic vehicles, atmospheric flight, ascent phase, trajectory optimization, convex programming