Design of Head Pursuit Guidance Law Based on Fractional-Order Sliding Mode Theory

This paper addresses problems on the interception of hypersonic vehicles in near-space. The main contribution is to study a head pursuit guidance law based on fractional-order sliding mode theory and analyze the stability of the guidance law provided. Firstly, the fractional-order differential operator, which has characteristics such as fast convergence and memory, is introduced into the design of sliding mode surface, based on which a head pursuit guidance can be designed to improve the performance of the guidance system. The stability of this guidance law is proved by Lyapunov stability theory. Based on this, a head pursuit guidance law considering autopilot dynamic characteristic is designed and the stability is also analyzed. Finally, numerical simulations are presented and the results verify that the guidance laws designed in this paper can avoid overload saturation at the initial moment of the terminal guidance stage and improve the convergence speed.