Optimal Impact Angle Guidance via First-Order Optimization Under Nonconvex Constraints

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.