Higher Order Sliding Mode Control by Keeping a 2-Sliding Constraint

This article investigates a new algorithm for higher order sliding mode control. The proposed control law keeps a constraint in 2-sliding mode such that the finite time stabilization of the chain of integrators is achieved. The proposed switching function has relative degree two with respect to the input and a second order sliding controller is used. The twisting controller is used for achieving finite time convergent 2-sliding mode to the switching manifold. The switching manifold is designed to provide finite time convergence of the integrator chain. The fractional powers in the switching function are carefully designed to prevent the unboundedness or singularity arising because of the switching constraint being kept at zero.