Aiming at the agile turn of air-to-air missile with thrust vector control(TVC),according to the features of TVC,a mechanical model of TVC is founded.The attitude angles vary in a wide range during agile turn,therefore it is required to establish six degree of freedom dynamics model by quaternion in order to avoid singularity caused by Euler angles.Taking the time-minimal as performance index, the thrust angles as control variables,and the attitude angles and the orientation of the missile velocity as ter-minal constraints,the model of optimal control problem of agile turn is established.Pseudospectral meth-od is applied to solve the optimal control for agile turn of a missile with TVC,and the optimal trajectory and the changing rule of the thrust angles meeting requirements are obtained.%针对推力矢量控制的空空导弹敏捷转弯问题,根据推力矢量控制的特点,建立推力矢量控制力学模型;由于敏捷转弯姿态角变化范围大,为避免欧拉角导致的奇异问题,用四元数法建立导弹的六自由度运动方程.以转弯时间最短为指标,以推力角为控制量,以导弹姿态和速度方向均达到指定角度为终端约束条件,建立敏捷转弯最优控制问题模型.以某使用推力矢量控制的空空导弹敏捷转弯为例,用伪谱法求解其最短时间内完成转弯所需的推力矢量控制,得到满足约束要求的最优弹道和推力角变化规律.
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