Application of multi-phase gauss pseudospectral method in optimal control for formation

In view of the formation coordinated attack time optimal control problem, formation coordinated attack mission is divided into three phases firstly, including formation formed, formation keeping and coordinated attack. Secondly, general motion equations in three phases have been established by simplifying delay and efficiency of control system. Then in combination with the mission characteristics of each phase, an optimal control model is put forward by separately considering anti-collision, expected formation, shift error, control limits, attack accuracy and other factors. To quickly solve the above optimal control problem, based on the Gauss pseudospectral method (GPM), the formation form - keep - attack integrated time optimal control algorithm is presented in this article. Finally, much of simulation work has been done to validate the effectiveness of the method and the simulation results demonstrate that the optimal control instruction can be quickly obtained by using this method under the condition of Legendre-Gauss (LG) nodes be selected reasonably, and the formation coordinated attack process can meet the demand of the task and the corresponding constraints.