An Improved Predefined-Time Adaptive Neural Control Approach for Nonlinear Multiagent Systems

This paper focuses on the predefined-time adaptive neural tracking control problem for nonlinear multiagent systems (MASs). In contrast to the existing results of the predefined-time control methods, this paper introduces a lemma for achieving predefined-time stability within the framework of backstepping, and the primary distinguishing feature is the ability to predefine the convergence time according to user specifications and the controller design process being influenced by a singular parameter. Meanwhile, a numerical example is presented by using the proposed lemma such that the convergence performance can be ensured by the user practical specification. Moreover, by using the neural networks (NNs) and the finite time differentiators, an adaptive approach to predefined-time tracking control is presented for nonlinear MASs. This method ensures the predefined-time stability of all signals within the MASs, while also enabling the followers&#x2019; outputs to accurately track the desired trajectory with the predefined time. The effectiveness and merits of the proposed scheme are substantiated through simulation results. <italic>Note to Practitioners</italic>&#x2014; This paper aims to address the predefined-time control problem for MASs, which can be widely used in practice, such as vehicular platoon systems control, teleoperation systems control, etc. The existing predefined-time methods only guarantee system convergence within the predefined-time interval, and achieving predefined-time convergence with an exact convergence time <inline-formula> <tex-math notation="LaTeX">$t$</tex-math> </inline-formula> remains a challenge. Moreover, the existing predefined-time methods contain many control parameters, which complicates the process of the parameter tuning. To address the aforementioned challenges, a predefined-time adaptive neural control method for MASs is developed, which can guarantee that all signals within MASs are predefined-time stable while enabling the followers to accurately track the desired trajectory with predefined time. Moreover, only one parameter and a pair of the finite time differentiators designed constants are involved in the controller design process, which simplifies the process of the parameter tuning.