Most of the optimal guidance problems can be formulated as nonconvex optimization problems, which can be solved indirectly by relaxation, convexification, or linearization. Although these methods are guaranteed to converge to the global optimum of the modified problems, the obtained solution may not guarantee global optimality or even the feasibility of the original nonconvex problems. In this paper, we propose a computational optimal guidance approach that directly handles the nonconvex constraints encountered in formulating the guidance problems. The proposed computational guidance approach alternately solves the least squares problems and projects the solution onto nonconvex feasible sets, which rapidly converges to feasible suboptimal solutions or sometimes to the globally optimal solutions. The proposed algorithm is verified via a series of numerical simulations on impact angle guidance problems under state dependent maneuver vector constraints, and it is demonstrated that the proposed algorithm provides superior guidance performance than conventional techniques.

翻译：大多数最优制导问题可表述为非凸优化问题，通常通过松弛、凸化或线性化方法间接求解。尽管此类方法能保证收敛至修正问题的全局最优解，但所得解可能无法保证原始非凸问题的全局最优性甚至可行性。本文提出一种直接处理制导问题中非凸约束的计算最优制导方法。该方法通过交替求解最小二乘问题并将解投影至非凸可行集上，可快速收敛至可行次优解，有时甚至获得全局最优解。针对状态相关机动矢量约束下的碰撞角制导问题，通过一系列数值仿真验证所提算法，结果表明该算法相比传统技术具有更优的制导性能。