Funnel Control for Uncertain Nonlinear Systems via Zeroing Control Barrier Functions

We consider the funnel-control problem for control-affine nonlinear systems with unknown drift term and parametrically uncertain control-input matrix. We develop an adaptive control algorithm that uses zeroing control barrier functions to accomplish trajectory tracking in a pre-defined funnel, achieving hence pre-defined transient and steady-state performance. In contrast to standard funnel-control works, the proposed algorithm can retain the system's input in pre-defined bounds without resorting to reciprocal terms that can lead to arbitrarily large control effort. Moreover and unlike the previous works on zeroing control barrier functions, the algorithm uses appropriately designed adaptation variables that compensate for the uncertainties of the system; namely, the unknown drift term and parametric uncertainty of the control-input matrix. Comparative computer simulations verify the effectiveness of the proposed algorithm.