通过对四旋翼飞行器进行动力学分析得到力学平衡方程，基于此建立了四旋翼飞行器的数学模型并得出其状态空间表达式。通过线性二次型设计控制系统，将开环不稳定系统构造成闭环稳定系统，并给出了线性二次型最优控制率表达式。为解决试验法难以确定最优加权矩阵的问题，利用遗传算法对线性二次型最优控制加权矩阵进行优化设计，寻找最优加权矩阵。通过Matlab以及Simulink，对基于遗传算法的四旋翼飞行器最优控制系统进行了仿真，并与基于试验法的线性二次型控制做对比。从仿真结果看，基于遗传算法的线性二次型最优控制使得四旋翼飞行器具有良好的动态性能。

Through a dynamic analysis of the quad-rotor aircraft,the mechanical equilibrium equation was set up,a mathematical model of the quad-rotor aircraft was established and its state space expression was obtained.The linear quadratic design was used to control the system,and the unstable open-loop system was constructed into a stable closed-loop system,and the linear quadratic optimal control expression was provided.In order to solve the problem that it is difficult to determine the optimal weighted matrix,the weighted matrix was optimized by using the Genetic Algorithm (GA),so that the optimal weighted matrix can be found out.The optimal control system of the quad-rotor aircraft was simulated on Matlab and Simulink,and was compared with the linear quadratic control based on the experimental method.The results show that:owing to the linear quadratic optimal control based on GA,the quad-rotor aircraft has nice dynamic performance.