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以time-to-go为基础建立时变的目标罚函数,根据最优控制理论,推导了对常值机动目标时变最优的增强型比例导引律;对权函数指数的分析结果表明,增强型比例导引有效导航比与权函数的指数一一对应。对增强型比例导引有效导航比的工程取值范围给出了合理的理论解释。将制导动力学简化为一阶滞后,并将导引头初始瞄准误差、目标常值机动引入到制导系统中,根据伴随法的数学思想,研究了增强型比例导引制导系统在初始瞄准误差、目标常值机动作用下的脱靶量解析解,最后通过伴随系统的数学仿真对解析解的正确性进行了验证。
Based on the time-to-go, a time-varying objective penalty function is established. According to the optimal control theory, an enhanced proportional guidance law is proposed to optimize the time-varying maneuvering target with constant time. The analysis of the weight function index shows that, Enhanced proportional navigation leads to a one-to-one correspondence with the index of the weight function. A reasonable theoretical explanation is given for the range of engineering of enhanced proportional guidance of effective navigation ratio. The guidance dynamics is reduced to a first-order lag, and the initial targeting error and the target constant maneuver of the seeker are introduced into the guidance system. According to the mathematical theory of adjoint method, the effects of the initial guidance error, The analytical solution of the miss distance of the target under constant maneuver, and the correctness of the analytical solution is verified by the mathematical simulation of the system.