Transition process-based low-complexity non-smooth funnel control for nonlinear MIMO systems

Most existing funnel control methods for nonlinear MIMO systems have a critical limitation: the initial tracking error must be within the funnel region to ensure system stability. This limitation reduces their practical applicability. This paper proposes a novel low-complexity non-smooth funnel control scheme that uses a transition process to decouple the funnel boundary design from the initial conditions, allowing for more flexibility in designing the funnel boundary irrespective of the initial error. The scheme also employs a non-smooth funnel transformation based on the transition error, which effectively reduces the tracking error to a smaller steady-state funnel region. The controller has a simple structure similar to a proportional controller, which makes it computationally efficient and easy to implement. Moreover, the controller incorporates a predefined time-convergent funnel boundary to guarantee that the tracking error converges to the steady-state funnel region within a user-specified time. These enhancements improve the robustness, adaptability, and tracking performance of the control system. The stability of the closed-loop system is rigorously established by Lyapunov theory, and the effectiveness of the proposed scheme is demonstrated by simulations and experiments of a SCARA robot.