Three-dimensional terminal angle constraint guidance law with class K_∞ function-based adaptive sliding mode control

This paper investigates the three-dimensional (3-D) interception guidance problem, where the missile is required to intercept the maneuvering target with the desired terminal angles. For the nonlinear relative kinematic model, a class K_∞ function-based adaptive sliding mode guidance law is proposed, which ensures that the errors of terminal Line-of-Sight (LOS) angles converge to the small neighborhoods of origin at the time of interception, without relying on information about the target's acceleration. To overcome the challenges of large initial control input and chattering in existing sliding mode guidance laws, two improved control schemes are introduced. The first scheme is to directly impose saturation constraints into the adaptive gain. However, it is important to ensure that the unknown disturbance remains within the prescribed saturation bound. To avoid the limitation, another approach involves introducing auxiliary dynamics to eliminate the reaching phase and slow down the convergence of LOS angles by presetting the convergence time of the sliding mode variables, which helps mitigate excessive initial control inputs. Numerical simulations are conducted using a realistic missile model and considering a 3-DOF point-mass aircraft as the target to evaluate three different guidance laws. The results indicate that the proposed guidance law ensures interception accuracy while substantially reducing the control gain.