关键词: 非线性控制系统, Lyapunov方法, 稳定性, 末制导律, H_∞控制

Abstract: For the case of three-dimensional interception, a new continuous nonlinear H_∞ guidance law with robustness is proposed. The mathematic model is built according to the three-dimensional relationship between the missile and the target whose acceleration is introduced as disturbance. Based on the method of zeroing the rate of the line-of-sight angle, a global nonlinear H_∞ control strategy is contrived to obtain the continuous nonlinear guidance law. The asymptotic stability of the guidance system is strictly proven by Lyapunov stability theory. Applying the method, it is unnecessary to solve the Hamilton-Jacobi-Isaacs (HJI) partial differential equation and control the relative velocity of the missile and the target. Finally an illustrative example is given to show that the new guidance law is more robust and suitable than the proportional navigation law for the missile to intercept a target with high velocity and high maneuverability, and that it is capable of achieving better precision of guidance.

Key words: nonlinear control systems, Lyapunov methods, stability, terminal guidance law, H_∞ control