Adaptive Event-Triggered Control for Nonlinear Systems With Asymmetric State Constraints: A Prescribed-Time Approach

Abstract

Finite/Fixed-time control yields a promising tool to optimize a system's settling time, but lacks the ability to separately define the settling time and the convergence domain (known as practically prescribed-time stability, PPTS). We provide a sufficient condition for PPTS based on a new piecewise exponential function, which decouples the settling time and convergence domain into separately user-defined parameters. We propose an adaptive event-triggered prescribed-time control scheme for nonlinear systems with asymmetric output constraints, using an exponentialtype barrier Lyapunov function. We show that this PPTS control scheme can guarantee tracking error convergence performance, while restricting the output state according to the prescribed asymmetric constraints. Compared with traditional finite/fixed-time control, the proposed methodology yields separately user-defined settling time and convergence domain without the prior information on disturbance. Moreover, asymmetric state constraints can be handled in the control structure through bias state transformation, which offers an intuitive analysis technique for general constraint issues. Simulation and experiment results on a heterogeneous teleoperation system demonstrate the merits of the proposed control scheme.

Observer-based practical predefined-time control for unmanned surface vehicles with guaranteed performance: A novel integral sliding mode approach

“…To handle this problem, a class of time-dependent scaling function (TDSF) based nonsingular predefined-time SMC is proposed for nonlinear systems [31], [41], [44], and the UBST appears as the sum of two predefined-time parameters. Further, Wang et al proposed a improved practical predefined-time stabilization (PPTS) theorem to ensure user-defined the settling time and convergence domain, simultaneously [45], but the convergence domain depends on the UBST. As for the USVs system, a few articles have been reported on the PTS problem, yet most of them mainly focus on formation/distributed control [46,47,48].…”

Fixed-time regulation of spacecraft orbit and attitude coordination with optimal actuation allocation using dual quaternion

“…The DQ-based modeling also becomes promising in spacecraft formation ( Nixon and Shtessel, 2022 ) and perception ( Srivatsan et al., 2016 ; Reynolds et al., 2020 ), whereas lacks the consideration of transient-state performance. As an important metric to evaluate transient-state convergence performance, settling time has gradually transformed from control objective to control parameter, thus allowing for more flexible control structures in terms of finite/fixed-time stability ( Bhat and Bernstein, 2000 ; Zhu et al., 2011 ; Polyakov et al., 2015 ; Chen et al., 2022 ; Wang et al., 2022 ). In terms of faster convergence performance and robustness against disturbances, recent works in ( Wang et al., 2020 ; 2019b ) have witnessed that terminal sliding mode control (TSMC) can provide a route for finite-time stability.…”