Prescribed-time tracking control for nonlinear systems with guaranteed performance

This paper studies the problem of the prescribed-time tracking control for a class of strict-feedback nonlinear systems with guaranteed performance. We will design a controller to achieve the following: one is to achieve the prescribed-time tracking, in which the settling time is not only independent of the design parameters, nor does it depend on the initial conditions, and can be set according to per our will; the other is to achieve prescribed performance composed of both the time-varying output constraint (TVOC) and the non-overshooting response. First, sufficient conditions on the prescribed-time tracking control with guaranteed performance are proposed. Then, based on the method of time-varying Barrier Lyapunov function (BLF) and LGV-backstepping, a recursive algorithm is developed to construct a controller to achieve the prescribed-time tracking control with guaranteed performance. Finally, two examples are provided to demonstrate the effectiveness of the proposed results.