基于分数阶微积分理论的最优导引律设计

随着技术的发展及战场环境的日益复杂化，拦截机动目标的需求越来越大。然而传统制导律在拦截机动目标时存在制导精度差、末端过载突变的问题，故提出了一种基于分数阶微积分理论的最优导引律。首先，介绍了分数阶微积分的定义、性质及其数字实现方法；然后，分析了弹目相对运动关系，通过分数阶变阶次建模和最优控制理论推导出了分数阶导引律；最后，仿真结果表明：与传统比例导引法相比，所设计的分数阶最优导引律能够保持比例导引法良好的追踪性能且拦截时间能够缩短2s，末端过载值趋近于0。该方法解决了传统比例导引法在末端由视线角速率发散而导致的末端过载突变问题。

Design of Active Disturbance Rejection Guidance Law for Attacking Maneuvering Target with Strapdown Seeker

With the development of technology and the increasing complexity of battlefield environment, the demand of intercepting maneuvering targets is increasing. However, the traditional guidance law has the limitations of guidance accuracy and terminal overload mutation when intercepting maneuvering targets. Therefore, an optimal guidance law based on fractional calculus theory is proposed in this paper. Firstly, the definition, properties and numerical implementation of fractional calculus are introduced. Then, the fractional order guidance law is derived by fractional order modeling and optimal control theory. Finally, the simulation results show that the fractional optimal guidance law designed in this paper could maintain the good tracking performance of the proportional guidance method, the interception time could be shortened by 2s, and the terminal overload value approaches to 0. It solves the problem of terminal overload mutation caused by the divergence of line of sight angular velocity in the traditional proportional guidance method.