基于Proximal-Newton-Kantorovich凸规划的空天飞行器实时轨迹优化

针对空天飞行器大气层内上升段实时轨迹优化问题，提出一种基于Proximal-Newton-Kantorovich凸规划的轨迹优化方法。首先，应用Newton-Kantorovich迭代方法将轨迹优化问题转化为一系列的子问题，每个子问题都是一个线性最优控制问题；其次，针对Newton-Kantorovich迭代方法忽略运动方程中的高阶信息，导致难以收敛这一问题，提出Proximal-Newton-Kantorovich迭代方法，在子问题的性能指标中加入邻近规则化项，改善了Newton-Kantorovich迭代方法的收敛性；最后，将子问题离散为二阶锥规划问题，并应用内点法进行求解。提出的Proximal-Newton-Kantorovich凸规划方法是一种求解非线性轨迹规划问题的可行途径。理论分析表明，Proximal-Newton-Kantorovich迭代方法的收敛结果一定是轨迹优化问题的局部最优解。数值实验表明，此方法的计算时间在毫秒级。

Real-time trajectory optimization for hypersonic vehicles with Proximal-Newton-Kantorovich convex programming

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.