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以描述编队飞行的相对运动方程为基础,根据线性定常系统的性质,采用最优控制理论和极小值原理设计了连续小推力作用下编队构型时间最短和燃料最省两种开关控制策略。仿真结果表明,由该方法得到的控制解能够满足线性定常系统最优控制的相关约束条件,证明了方法的正确性和有效性。与传统的有限推力最优编队构型控制方法相比,该方法不需要求解复杂的两点边值问题,仅描述运动状态转移的非线性方程组即可得到最优控制策略,具有形式简单、计算量小、利于实施等优点。
Based on the description of the relative motion equation of formation flying, according to the property of linear steady system, the optimal control theory and minimum principle are used to design the switching control strategy with the shortest formation time and the most fuel saving under the action of continuous small thrust. The simulation results show that the control solution obtained by this method can satisfy the relevant constraints of the optimal control of linear steady-state system and prove the correctness and effectiveness of the method. Compared with the traditional optimal thruster formation control method, this method does not need to solve the complex two-point boundary value problem. It can obtain the optimal control strategy by describing only the nonlinear equations of motion state transition, and has the advantages of simple form, Small amount of calculations, conducive to the implementation of the advantages.