Prescribed-time tracking with prescribed performance for a class of strict-feedback nonlinear systems

In this paper, we will investigate the prescribed-time tracking with prescribed performance for a class of strict-feedback nonlinear systems. A control strategy will be proposed to achieve the tracking error constrain by prescribed performance bound (PPB) and converge to zero in prescribed-time. The PPB constrains not only the convergence rate, but also the maximum overshoot of the tracking error. The tracking error will converge to zero in prescribed-time. Such a prescribed-time is irrespective of both initial conditions and design parameters. First, by incorporating the PPB into the original system via a transformation, a equivalently transformed system is obtained, which is unconstrained and convenient for control design. Then, with the help of backstepping, a controller is recursively designed to guarantee that the tracking error satisfies the PPB all the time and converges to zero in prescribed-time. The key to designing the controller is that a fractional term is introduced when designing the virtual stabilizing function during each step of backstepping, which in turn decreases the Lyapunov function to origin within prescribed-time. Finally, two examples are presented to demonstrate the validity of our proposed control strategy.