Design of constrained adaptive backstepping guidance law

For the terminal guidance problem of missiles intercepting maneuvering target with impact angle constraint, autopilot lag and acceleration command saturation constraint, a constrained adaptive backstepping guidance law is developed based on a command filtered backstepping control method and adaptive control, and the second-order dynamics of missile autopilot with the external disturbance is considered. By use of the command filter, the designed guidance law can not only deal with the saturation constraint on the acceleration command but also overcome the term explosion of traditional backstepping method. By virtue of adaptive control, the proposed guidance law is able to estimate the upper bound of external disturbance. And, the proposed guidance law using the hyperbolic tangent function is continuous and hence, the chattering problem caused by the use of signum function in the existing traditional sliding mode control guidance law can be avoided. Theoretical analysis shows that the proposed guidance law can guarantee that the line-of-sight (LOS) angular rate asymptotically converges to zero and the LOS angle also asymptotically converges to the desired terminal LOS angle. Numerical simulations are presented to demonstrate the effectiveness of the proposed guidance law.