Fixed-time ASOSM controller design for output-constrained systems with mismatched terms

This paper investigates the controller design of fixed-time adaptive second-order sliding mode (ASOSM) under mismatched terms and asymmetric output constraints. First, the problem of the asymmetric output constraint is addressed through building a barrier Lyapunov function. Subsequently, by applying the backstepping-like technique, the ASOSM controller is methodically designed via a stepwise procedure. Notably, the controller involves an adaptive parameter, which is acquired by the developed adaptive mechanism. The mechanism aims at resolving the disturbances with unknown magnitudes. It has been validated that the system states can be regulated to zero within a fixed time, which insinuates that the settling time is independent of initial conditions. Moreover, the proposed approach effectively mitigates uncertainties in the control channel. Finally, a numerical example is presented to confirm the validity of the proposed ASOSM controller.