Data-Driven Control With Prescribed-Time Convergence for Discrete-Time Nonlinear Systems

Abstract

In this paper, the issue of data-driven prescribed-time convergence control for certain types of discrete-time nonlinear systems is investigated. The dynamic linearization technique and the discrete prescribed-time gain-scheduled feedback function have been combined to create a model-free adaptive prescribed time control strategy. To keep the steady-state error within a bespoke steady-state error band, the controller is switched to a steady-state controller once the system has completed its prescribed time control task. Theoretically, it is demonstrated that the error dynamics can gradually compress from the initial error to the steady-state error band during the initial and prescribed time periods. Furthermore, all of the rule designs in this study are data-driven and solely rely on system input and output data. Manipulator experiments and numerical modeling demonstrate the viability of the proposed strategy.Note to Practitioners—The motivation for this paper stems from the need to design a prescribed-time control method for the industrial robot trajectory tracking control tasks. Prescribed-time control method offers a potential to improve both the speed and coordination of industrial robot trajectory tracking. However, due to the increasing complexity of the robot structure and operating environment, it has brought great difficulties to the use of model-based prescribed-time control. To address this issue, a data-driven prescribed-time control approach is proposed, the controller design and convergence proof through mathematical derivations are also provided. Finally, the effectiveness of the proposed control scheme is validated through numerical simulations and industrial robotic manipulator experiments. This research contributes a viable and efficient time-optimal control method for trajectory-tracking tasks in the realm of industrial robotics.