This paper proposes an optimal midcourse guidance method for dual pulse air-to-air missiles,which is based on the framework of the linear Gauss pseudospectral model predictive control method.Firstly,a multistage optim...This paper proposes an optimal midcourse guidance method for dual pulse air-to-air missiles,which is based on the framework of the linear Gauss pseudospectral model predictive control method.Firstly,a multistage optimal control problem with unspecified terminal time is formulated.Secondly,the control and terminal time update formulas are derived analytically.In contrast to previous work,the derivation process fully considers the Hamiltonian function corresponding to the unspecified terminal time,which is coupled with control,state,and costate.On the assumption of small perturbation,a special algebraic equation is provided to represent the equivalent optimal condition for the terminal time.Also,using Gauss pseudospectral collocation,error propagation dynamical equations involving the first-order correction term of the terminal time are transformed into a set of algebraic equations.Furthermore,analytical modification formulas can be derived by associating those equations and optimal conditions to eliminate terminal error and approach nonlinear optimal control.Even with their mathematical complexity,these formulas produce more accurate control and terminal time corrections and remove reliance on task-related parameters.Finally,several numerical simulations,comparisons with typical methods,and Monte Carlo simulations have been done to verify its optimality,high convergence rate,great stability and robustness.展开更多
In the field of calculating the attack area of air-to-air missiles in modern air combat scenarios,the limitations of existing research,including real-time calculation,accuracy efficiency trade-off,and the absence of t...In the field of calculating the attack area of air-to-air missiles in modern air combat scenarios,the limitations of existing research,including real-time calculation,accuracy efficiency trade-off,and the absence of the three-dimensional attack area model,restrict their practical applications.To address these issues,an improved backtracking algorithm is proposed to improve calculation efficiency.A significant reduction in solution time and maintenance of accuracy in the three-dimensional attack area are achieved by using the proposed algorithm.Furthermore,the age-layered population structure genetic programming(ALPS-GP)algorithm is introduced to determine an analytical polynomial model of the three-dimensional attack area,considering real-time requirements.The accuracy of the polynomial model is enhanced through the coefficient correction using an improved gradient descent algorithm.The study reveals a remarkable combination of high accuracy and efficient real-time computation,with a mean error of 91.89 m using the analytical polynomial model of the three-dimensional attack area solved in just 10^(-4)s,thus meeting the requirements of real-time combat scenarios.展开更多
协方差分析描述函数法(covariance analysis describing function technique,CADET)在处理系统的随机响应问题上具有求解迅速、仿真精度高等优点.但对于复杂系统,其理论推导过程、求解系统解析响应方程较为复杂繁琐.为进一步推广CADET...协方差分析描述函数法(covariance analysis describing function technique,CADET)在处理系统的随机响应问题上具有求解迅速、仿真精度高等优点.但对于复杂系统,其理论推导过程、求解系统解析响应方程较为复杂繁琐.为进一步推广CADET的应用,依托高斯–埃尔米特积分法,提出了一种通用化的CADET数值算法.作为算法验证,以车辆行驶过程中的随机振动为例,建立了几种不同非线性悬架车辆的二自由度动力学模型,并将CADET通用化数值算法与传统CADET算法及蒙特卡罗法进行了对比分析.仿真结果表明,CADET的通用化数值算法可以达到满足应用要求的计算精度,这验证了所提数值算法的有效性,且具有更强的泛化应用于复杂非线性动力系统的价值.展开更多
基金supported by the National Natural Science Foundation of China(No.62003019)the Young Talents Support Program of Beihang University,China(No.YWF-21-BJ-J-1180).
文摘This paper proposes an optimal midcourse guidance method for dual pulse air-to-air missiles,which is based on the framework of the linear Gauss pseudospectral model predictive control method.Firstly,a multistage optimal control problem with unspecified terminal time is formulated.Secondly,the control and terminal time update formulas are derived analytically.In contrast to previous work,the derivation process fully considers the Hamiltonian function corresponding to the unspecified terminal time,which is coupled with control,state,and costate.On the assumption of small perturbation,a special algebraic equation is provided to represent the equivalent optimal condition for the terminal time.Also,using Gauss pseudospectral collocation,error propagation dynamical equations involving the first-order correction term of the terminal time are transformed into a set of algebraic equations.Furthermore,analytical modification formulas can be derived by associating those equations and optimal conditions to eliminate terminal error and approach nonlinear optimal control.Even with their mathematical complexity,these formulas produce more accurate control and terminal time corrections and remove reliance on task-related parameters.Finally,several numerical simulations,comparisons with typical methods,and Monte Carlo simulations have been done to verify its optimality,high convergence rate,great stability and robustness.
基金National Natural Science Foundation of China(62373187)Forward-looking Layout Special Projects(ILA220591A22)。
文摘In the field of calculating the attack area of air-to-air missiles in modern air combat scenarios,the limitations of existing research,including real-time calculation,accuracy efficiency trade-off,and the absence of the three-dimensional attack area model,restrict their practical applications.To address these issues,an improved backtracking algorithm is proposed to improve calculation efficiency.A significant reduction in solution time and maintenance of accuracy in the three-dimensional attack area are achieved by using the proposed algorithm.Furthermore,the age-layered population structure genetic programming(ALPS-GP)algorithm is introduced to determine an analytical polynomial model of the three-dimensional attack area,considering real-time requirements.The accuracy of the polynomial model is enhanced through the coefficient correction using an improved gradient descent algorithm.The study reveals a remarkable combination of high accuracy and efficient real-time computation,with a mean error of 91.89 m using the analytical polynomial model of the three-dimensional attack area solved in just 10^(-4)s,thus meeting the requirements of real-time combat scenarios.
文摘协方差分析描述函数法(covariance analysis describing function technique,CADET)在处理系统的随机响应问题上具有求解迅速、仿真精度高等优点.但对于复杂系统,其理论推导过程、求解系统解析响应方程较为复杂繁琐.为进一步推广CADET的应用,依托高斯–埃尔米特积分法,提出了一种通用化的CADET数值算法.作为算法验证,以车辆行驶过程中的随机振动为例,建立了几种不同非线性悬架车辆的二自由度动力学模型,并将CADET通用化数值算法与传统CADET算法及蒙特卡罗法进行了对比分析.仿真结果表明,CADET的通用化数值算法可以达到满足应用要求的计算精度,这验证了所提数值算法的有效性,且具有更强的泛化应用于复杂非线性动力系统的价值.
