Barrier Function-Based Adaptive Composite Sliding Mode Control for a Class of MIMO Underactuated Systems Subject to Disturbances

This article proposes the design and verification of a novel barrier function (BF)-based adaptive composite sliding mode control method dedicated to the multiple-inputs–multiple-outputs underactuated systems. The proposed scheme is constructed by a composite sliding mode surface along with dual adaptive parameters. The main advantage of this scheme is that the actuated and underactuated state errors are integrated on the same proportional-integral-differential sliding mode surface, which not only enhances the coupling between the actuated and underactuated states, but also introduces an integral term in the sliding mode surface to improve performance of the system. In addition, a novel adaptive scheme of BF is proposed, which ensures that the system is bounded to converge and the range of the boundary can be set artificially even though the upper bounds of the external disturbances and the nonlinear phenomenon of the actuator are unknown. Rigorous stability analysis, based on the Lyapunov function, demonstrates the convergence of the composite sliding mode surface as well as all error states within the system. Finally, the proposed control algorithm is validated for its effectiveness and practicality through experimental results obtained from a four-degrees of freedom tower crane system.