Transition-Enhanced Funnel Control for Nonlinear MIMO Systems With Discontinuous References

Traditional funnel control faces challenges with discontinuous reference signals, leading to instability and degraded control performance. To address these limitations, this article proposes a transition-enhanced funnel control method that ensures stability even when tracking errors exceed the funnel boundary. The proposed approach incorporates a transition-enhanced mechanism that transforms tracking errors influenced by discontinuities into transition errors initialized at zero. These transition errors are then smoothly reverted to the original errors within a predefined time. Moreover, an adaptive predefined-time funnel region is introduced, which resets to its maximum initial value at each discontinuity. This reset reduces the control input magnitude and enhances system robustness. A computationally efficient funnel controller ensures that the transition errors remain within the funnel region while the tracking errors converge to the steady-state funnel region within a user-defined time after each discontinuity, thereby guaranteeing tracking performance. A Lyapunov-based analysis guarantees closed-loop stability, and simulations and experiments validate the effectiveness of the proposed method.