Low-Complexity Non-Smooth Funnel Control: A Transition Function-Based Approach for Nonlinear MIMO Systems

This paper presents a non-smooth funnel control approach with low complexity for nonlinear MIMO systems. The proposed technique incorporates a transition function, which eliminates the dependence on initial conditions and allows for the flexible design of the funnel boundary. The controller leverages a predefined-time convergence funnel region to ensure that the tracking error converges to the steady-state funnel region within a user-specified time. Additionally, a non-smooth funnel transformation is applied, substantially minimizing the tracking error to a more compact steady-state funnel region. Furthermore, the controller's simple structure ensures computational efficiency and ease of implementation. The stability of the closed-loop system is proven through Lyapunov theory, and the proposed approach's effectiveness is demonstrated through simulations on a second-order MIMO system and experimental tests with a SCARA robot.