Finite/fixed/predefined/exact time control: a unified framework

This paper investigates the settling time problem for dynamical systems, and some novel results are proposed. First, by reviewing classic achievements about the settling time problem of the control system, a new framework is designed. Then, based on the proposed framework, the classic fixed time control scheme is improved to predefined time control and exact time control results, respectively. Similarly, finite time control scheme is transformed into predefined time control and exact time control results. Furthermore, considering the bounded control results are vital in actual applications, the novel predefined time-bounded control and exact time-bounded control schemes are given. In the end, numerical simulations are conducted for robotic manipulators to demonstrate the effectiveness of the developed control strategies.