中文摘要：

对于拦截机动目标问题,传统方法中基于Lyapunov稳定性理论获得的导引规律,在数学原理上只能保证当时间趋于无穷时视线角速率趋于零。基于非线性控制系统有限时间稳定性理论,提出了制导系统有限时间收敛的充分条件和一种形式简洁的有限时间收敛变结构导引规律。证明了在目标-导弹相对接近速度为常数,而且目标机动条件下,该导引律令视线角速率在末制导结束前收敛到零。最后以某拦截问题为实例对导引律的有限时间收敛性质进行了数学仿真验证。

英文摘要：

For interception of maneuvering targets, mathematically speaking, the guidance laws based on traditional Lyapunov stability theory can only nullify the line of sight angular rate when time approaches infinity. Based on finite time stability theory of nonlinear control systems, a sufficient condition of finite time convergence of guidance system is given and a concise finite time convergent variable structure guidance law is proposed. Assume the relative velocity between the target and the missile is approxi- mately constant. For intercepting the maneuvering target, the guidance law can ensure that the line of sight angular rate converge to zero before the final time of interception. The finite time convergence property by the guidance law is verified by simulation.