Design a Guidance Law Considering Approximation of Missile Control Loop Dynamics Using Adaptive Back-Stepping Theory

In this paper, a new guidance law is designed to improve the performance of a homing missiles guidance system in terminal phase. For this purpose first of all, the two dimensions equations of motion are formulated, then the approximation dynamic of missile control loop is added to these equations which are nonlinear whit unmatched uncertainty. Then, a new adaptive back-stepping method is developed in order to control this system. An adaptive term is used in the control law that is converged to the uncertainty. This convergence is proved based on Lyapunov stability theorem. Therefore using this adaptive term in the control law can be eliminated the uncertainty. Based on this algorithm, a new guidance law is designed. Then its performance is compared with common guidance laws in a guidance loop simulation in the presence of control loop dynamics