Constraints Maintaining Mesh Refinement Method for Solving Whole Trajectory of Discontinuous Aerodynamics

Abstract

Solving trajectories of multi-phase dynamic advanced vehicles is difficult due to the coexistence of discontinuous aerodynamics, long-range and multi-peak features. Despite traditional phase-by-phase solving method for trajectory is expressive and easy to optimize, it loses global optimality to some extent and the state estimation between phases is cumbersome. In contrast, an all-in-one solution method for the whole trajectory can carry out global search and avoid the inter-phase state estimation, but the expression of the problem formulation is more complicated, and it is difficult to converge to a feasible solution. In this paper, we formulate the whole trajectory solving problem based on a representative vehicle and propose a constraints maintaining mesh refinement method based on the pseudo-spectral method to solve the whole trajectory allin-one. First, the proposed method presets a knot on the trajectory to construct an optimal control problem with a two-phase dynamic constraint, which maintains continuity of variables between the discontinuous aerodynamics. Second, ph-refinement is used to deal with long-range and multi-peak features throughout the trajectory. Third, to make mesh refinement and iterative solution feasible under discontinuous aerodynamics, an interval extending operator is proposed to maintain the consistency of constraints during the process of mesh refinement. Finally, the effectiveness of the proposed method for solving the whole trajectory is verified by 7 comparison experiments. The results show that the proposed method can effectively handle the whole trajectory problem of discontinuous aerodynamics, as evidenced by feasibility, convergence, optimality, and superiority.INDEX TERMS hypersonic vehicles; optimal trajectory; mesh refinement; discontinuous aerodynamics