Pre and Post Optimality Checking of the Virtual Motion Camouflage based Nonlinear Constrained Subspace Optimal Control

Nonlinear constrained trajectory optimization remains an active field of research. Current popular methods end up with either solving a classical multi-dimensional two-point boundary value problem or a high dimensional nonlinear programming problem. Inspired by the motion camouflage phenomenon of insects like dragonflies, recently the authors proposed a subspace optimization method, the virtual motion camouflage method, in order to reduce the problem dimension. Thus the computational cost experienced in the widely used direct collocation and nonlinear programming methods can be reduced. The solution found through this approach is in the feasible region however the optimality of the solution is not guaranteed automatically in the original full search space. In this paper, two optimality checking ways extended from the Karush-Kuhn-Tucker necessary condition are proposed. The pre-optimality checking is proposed to judge the selection of the virtual prey motion and the reference point, while a post-optimality checking is suggested to test the solution obtained from the virtual motion camouflage method in the original search space. Two numerical examples are used to illustrate the capabilities of the new subspace optimal control algorithm.