Prescribed-Time Tracking With Guaranteed Transient Performance for Strict-Feedback Nonlinear Systems

This paper researches the prescribed-time tracking (PTT) with guaranteed transient performance for a class of nonlinear systems. The guaranteed transient performance means that the tracking error would be constrained with a pair of decaying exponential bounds. First, by introducing a convergence-invariant unbounded transformation, a new transformed system is given by incorporating the prescribed performance bounds (PPBs) into the original system. Second, the control law is designed by backstepping technique with the quadratic Lyapunov function, in which a fractional term plays a significant role in accomplish PTT with guaranteed transient performance. Then, the PTT with guaranteed transient performance is achieved, and the output tracking error converges to zero within prescribed time and remains at equilibrium thereafter, while the boundedness of all closed-loop signals is assured. Finally, two examples are given to illustrate the effectiveness of the proposed results.