提出一种新颖的无人机三维追逃问题的求解方法,该方法结合变分法和伪谱法,是一种半直接法求解思想。求解过程首先应用变分法给出求解一个局中人最优控制律的微分方程组及其约束条件,将微分对策问题转换为最优控制问题,然后通过伪谱法再将最优控制问题转换成非线性规划问题,最后利用SNOPT求解器对其进行数值求解,并进行了数值仿真。对仿真结果的分析表明,追逃双方在博弈过程中都采取了各自最优的控制策略,验证了该方法的正确性、有效性和快速性。 A novel method to solve the three-dimensional pursuit of UAV is proposed. This method, combined with variational method and pseudospectral method, is a semi-direct method. In the process of solving, first of all, the system of differential equations and its constraints for solving the optimal control law of an agency are given by using the variational method, and the differential game problem is transformed into the optimal control problem. Then the optimal control problem is transformed Into a nonlinear programming problem, and finally use the SNOPT solver to solve the numerical problem and carry out numerical simulation. The analysis of the simulation results shows that both pursue each other in the game have taken their own optimal control strategy to verify the correctness, effectiveness and speed of the method.