基于自适应最优控制的有限时间微分对策制导律

Finite-time differential guidance law based on adaptive optimal control

针对固定末端时刻拦截机动目标的制导系统,本文首先构建了非线性有限时间微分对策框架,将导弹拦截非线性系统的最优问题转化为一般非线性系统的最优控制问题,并通过自适应动态规划算法(adaptive dynamic programming,ADP)获得近似最优值函数与最优控制策略.为了有效实现该算法,本文利用一个具有时变权值和激活函数的评价网络来逼近Hamilton-Jacobi-Isaacs(HJI)方程的解,并在线更新.通过李雅普诺夫法来证明本文提出的控制策略可保证闭环微分对策系统稳定性和评价网络权值近似误差的有界性.最后给出一个非线性导弹拦截目标系统的仿真例子验证了该方法的可行性和有效性.

In this paper,the problem of intercepting a maneuvering target within a fixed final time is posed in a nonlinear finite-time differential game framework.Then,we convert the optimal problem of nonlinear guidance system into optimal control problem of general nonlinear system.For this system,the approximate optimal function and optimal control strategy are found by solving the finite-time differential game problem via adaptive dynamic programming (ADP) technique. To implement the algorithm effectively,the single critic network with time-varying weights and activation functions is constructed to estimate the solution of associated time-varying Hamilton-Jacobi-Isaacs (HJI) equation,and update it online.By utilizing the Lyapunov stability theorem,the closed-loop differential game system are proved to be stable and the estimation weight error of the critic network are proved to be uniformly ultimately bounded.Finally,a simulation of a nonlinear missile-target interception system shows the feasibility and effectiveness of the proposed method.