Research on a Differential Geometric Guidance Law Based on Fractional-Order Theory

In this paper, fractional-order calculus theory is used to investigate the geometric law for intercepting an agile target. In order to overcome the challenges presented by the divergence of line of sight rate (LOSR) of proportional navigation (PN), the fractional LOSR is used as a compensated term in the proposed fractional differential geometric guidance law (FDGGL). By adjusting the navigation gain of the FDGGL, the new proposed guidance law can be transformed into the traditional differential geometric guidance law (DGGL) and PN. The average overload and ballistic stability of the FDGGL are analyzed based on the fractional and control theory. Some analytical results about energy consumption and trajectory variation of the FDGGL were obtained. The simulation results shows that, compared with PN and DGGL, the FDGGL has better guidance performance when intercepting different maneuvering targets.