Stabilization of an underactuated parallel system with a single input

A novel sliding mode control (SMC) strategy is presented in this paper for a class of parallel underactuated nonlinear systems, where a single scalar control input simultaneously affects multiple states. A key challenge in the control design for this class of systems is that standard backstepping-based approaches cannot be applied. This difficulty is mitigated through innovative selection of a sliding surface, along with a novel sequential control design procedure. The proposed control method is continuous, and it is designed to be computationally minimal, requiring no observers, function approximators, or online adaptive laws. The proposed control law achieves asymptotic regulation of multiple states using a scalar control input. A rigorous stability analysis is provided to prove the theoretical result, and numerical simulation results based on an inverted pendulum system are provided to demonstrate the effectiveness of the proposed control algorithm.