Predefined-Time Convergence Terminal Sliding Mode Guidance Laws Against Angle Constraints

This paper proposes three-dimensional impact angle control guidance laws based on a predefined-time convergence sliding mode control scheme. Unlike the usual decoupling design approach, the guidance laws are derived from strong coupled engagement dynamics, and the guidance commands are formulated in terms of the missile’s lateral accelerations rather than the tangential accelerations of the lineof-sight. A predefined-time convergence terminal sliding mode is presented to enforce the desired impact angle precisely at the time of interception. Since the traditional reaching control is prone to arouse actuator saturation despite small initial errors, a double surfaces approach is proposed to manage the reaching phase. The corresponding guidance law realizes a whole global sliding mode, and enforces that the original sliding variable converge to zero within a predefined time. The stability of the guided system is analyzed with Lyapunov stability theory. The property of predefined-time convergence is demonstrated via analytic solutions. Numerical simulation results are presented to validate the proposed guidance laws for a constant, as well as realistic missile model.