Nonsingular continuous finite-time convergent guidance law with impact angle constraints

This paper documents a novel nonsingular continuous guidance which can drive the line-of-sight (LOS) angular rate to converge to zero in finite time in the presence of impact angle constraints. More specifically, based on the second-order sliding mode control (SMC) theory, a second-order observer (2-OB) is presented to estimate the unknown target maneuvers, while a super twisting algorithm- (STA-) based guidance law is presented to restrict the LOS angle and angular rate. Compared with other terminal sliding mode guidance laws, the proposed guidance law absorbs the merits of the conventional linear sliding mode (LSM) and terminal sliding mode (TSM) and uses switching technique to avoid singularity. In order to verify the stability of the proposed guidance law, a finite-time bounded (FTB) function is invited to prove the boundedness of the proposed observer-controller system and a Lyapunov approach is presented to prove the finite-time convergence (FTC) of the proposed sliding system. Rigorous theoretical analysis and numerical simulations demonstrate the mentioned properties.