Global Funnel Control of Nonlinear Systems with Unknown and Time-Varying Fractional Powers

This paper is concerned with the global funnel control (FC) issue of the nonlinear systems with unknown dynamics and time-varying fractional powers. An FC strategy is proposed in this paper, not only the barrier functions but also the tracking and intermediate errors are introduced to our control law in a proportional feedback way, which not only guarantees uniform performance insurance under any initial condition of the control system but also leads to about 50% reduction in control amplitude with respect to the existing solutions. Moreover, it exhibits notable simplicity, with no need for parametric details of time-varying fractional powers, adding a power integrator technique, parameter identification, function approximation or derivative calculation. A comparative simulation demonstrates the effectiveness and superiority of the developed method.