A novel non-uniform optimal control approach for hypersonic cruise vehicle with waypoint and no-fly zone constraints

Dynamic optimisation for hypersonic cruise vehicle (HCV) is a challenge for the complex nonlinear constraints with waypoint and no-fly zone during a global strike mission. Because the passing time of each waypoint is unknown, it is difficult to guarantee the precision of waypoint constraints on non-collocation points for traditional pseudospectral method. A novel optimal control approach is therefore proposed, where waypoints are firstly transformed into variable optimisation parameters of pseudospectral method, which can satisfy the waypoint constraints completely. Then, a novel non-uniform pseudospectral approach with mesh refinement is further proposed by introducing the adaptive gradient analysis to provide a time grid iteratively. With this refinement, the proposed approach needs fewer computational time to achieve better performance of accuracy compared with traditional uniform refinement pseudospectral method. The proposed approaches are finally applied to a classic HCV problem with waypoints and no-fly zone constraints and compared with other methods reported in literature in detail. The research results validate both the effectiveness and the time saving benefit of the proposed methods.