基于Nussbaum-type增益技术的末制导律设计

Designing a New and Better Terminal Guidance Law Based on Nussbaum-Type Gain Technique

针对三维目标拦截问题,文章提出了一种新的具有强鲁棒性的非线性末制导律。基于弹目相对运动学的非线性关系,将目标机动作为系统的有界扰动,建立了三维弹目相对运动的数学模型。并应用Nussbaum-type增益技术,基于零化弹目视线角速率的思想,提出了一种全局非线性稳定控制策略,得到了连续的非线性末制导律。该方法利用Lyapunov稳定理论严格证明了在有限时间内弹目视线角速率收敛到适当小的范围内,实现末制导系统的稳定性。数字仿真表明和比例导引律相比,这种制导律对高速大机动目标具有很强的鲁棒性和适应性,并能获得良好的制导精度。

Aim.The introduction of the full paper reviews Refs.1 through 9 and then proposes the design of what we believe to be a new and better terminal guidance law.Sections 1 and 2 explain our design;their core consists of：（1） we build the mathematical model for three-dimensional interception according to the relative motion relationship between the interception missile and its target;（2） we employ the Nussbaum-type gain technique and the idea of zeroing the rate of line-of-sight angle to design the continuous nonlinear terminal guidance law;（3） we prove the stability of the terminal guidance system by using the Lyapunov stability theory and attempt to zero the product ab,where a is the line-of-sight rate and b is the relative distance between the missile and its target within the limited time.Section 3 simulates our terminal guidance law;the simulation results,presented in Figs.2 through 4 and Table 1,and their analysis show preliminarily that our new and better terminal guidance law is indeed more robust and suitable for the missile that intercepts the target of high velocity and high maneuver than the conventional optimal proportional navigation law and that our terminal guidance law is of better precision.