Global Prescribed-Time Second-Order Sliding Mode Controller Design Subject to Asymmetric Output Constraint

In this work, a prescribed-time second-order sliding mode (SOSM) controller is constructed to address a class of nonlinear systems in the presence of asymmetric output constraints. To handle the asymmetric constraints, a frequently-used asymmetric barrier Lyapunov function is employed. Meanwhile, a time-varying scaling function is introduced to ensure the prescribed-time convergence of the closed-loop sliding mode system. On this basis, a prescribed-time SOSM controller is constructed by inserting the asymmetric BLF and time-varying scaling function into a modified power integrator technique. The rigorous theoretical analysis indicates that under the proposed prescribed-time SOSM control scheme, the overall system is prescribed-time stable without violating the asymmetric constraints. The distinguishing feature is that the convergence time of the overall system can be specified beforehand and does not depend on any system initial conditions. Finally, an academic simulation example is provided to demonstrate the effectiveness of the presented prescribed-time control scheme.