三体对抗中的主动防御鲁棒最优预测制导律研究  

Robust Optimal Predictive Guidance Law for Active Defense in Three-Body Confrontation

作　　者：陈维义[1] 何凡 李逸源 董海迪 CHEN Weiyi;HE Fan;LI Yiyuan;DONG Haidi(Department of Ordnance Engineering,Naval University of Engineering,Wuhan,Hubei 430030,China)

机构地区：[1]海军工程大学兵器工程学院,湖北武汉430030

出　　处：《北京理工大学学报》2024年第6期645-654,共10页Transactions of Beijing Institute of Technology

基　　金：国家自然科学基金资助项目(62101579)。

摘　　要：考虑防御导弹和我方目标控制系统内部扰动和未准确建模动态特性等因素造成的不确定性影响,设计了鲁棒最优预测制导律(robust optimal predictive guidance law,ROPGL)和鲁棒协同最优预测制导律(robust cooperative optimal predictive guidance law,RCOPGL)拦截来袭寻的导弹.首先,通过对非线性运动学方程线性化和降阶得到简化后的标称系统的状态方程;其次,考虑控制系统的不确定性,建立鲁棒制导问题的模型;再次,基于动态规划方法得到最优制导问题的制导指令关系式,并利用李雅普诺夫稳定性理论证明了最优制导问题的制导指令能够使鲁棒制导问题稳定;然后,引入界值函数得到线性二次型最优制导问题,通过求解黎卡提矩阵微分方程得到制导指令;最后,对设计的制导律的性能进行仿真验证.仿真结果表明,相比于其他制导律,设计的制导律能够抑制不确定性的影响,实现防御导弹对寻的导弹的拦截.In order to intercept incoming homing missile accurately,a robust optimal predictive guidance law(ROPGL)and a robust cooperative optimal predictive guidance law(RCOPGL)were proposed in this paper,considering some uncertain factors caused by internal disturbances and inaccurate modeling for dynamic characteristics of defender and target control system.Firstly,a simplified state equation of the nominal system was established based on linearization and order-reduction of the nonlinear kinematic equation.And considering the uncertainties of the actual control system,an expression model was established for the robust guidance problem.Accordingly,an expression of the guidance command was obtained based on the dynamic programming method for the optimal guidance,and the guidance command was proved with Lyapunov stability theory to be capable of make the robust guidance problem stabilize.And then,introducing a boundary value function to handle the linear quadratic optimal guidance problem,the guidance command was obtained by solving the Riccati matrix differential equation.Finally,a simulation was carried out to verify the performance of the designed guidance law.The results show that compared with other guidance laws,the designed guidance law can suppress the influence of uncertainties and complete the accurate interception.

关 键 词：最优制导 预测制导 鲁棒性 不确定性 主动防御 

分 类 号：TJ765.3[兵器科学与技术—武器系统与运用工程]