Abstract
Achieving a rapid dynamic response is of critical importance in nonlinear system control. This paper develops a generalized adjustable predefined-time (GAPT) control and observation scheme for second-order nonlinear dynamical systems, aiming to overcome the limitation of non-adjustable actual convergence time in traditional predefined-time methods. Firstly, a novel GAPT system framework is proposed. This framework promotes the concept of traditional predefined time systems and introduces an adjustment parameter to flexibly adjust the actual convergence time of the system. Secondly, an adaptive generalized adjustable predefined-time observer (AGAPTO) is designed, which combines adaptive laws to ensure that the observation error converges to the specified boundary within a predefined time, while the disturbance estimation error achieves exponential convergence. Thirdly, a nonsingular generalized adjustable predefined-time sliding mode controller (NGAPTSMC) is proposed. This controller not only addresses the singularity issue of traditional predefined-time sliding modes, but also utilizes the GAPT characteristics to achieve adjustability of the actual convergence time for the arrival and switching stages. The effectiveness and superiority of the proposed method are validated through numerical simulations and real-time experiments. Note to Practitioners—In nonlinear system control, achieving fast dynamic response is crucial. This paper investigates the predefined-time control of nonlinear systems. The proposed control method can be applied to common nonlinear systems, such as inverted pendulums, mobile robots, autonomous aerial vehicles, robotic manipulators, etc. While traditional predefined-time control methods guarantee convergence within a pre upper limit, the actual convergence time becomes difficult to flexibly adjust once this limit is determined. To address this, this paper proposes a novel generalized adjustable predefined-time (GAPT) system framework. By intro...