Abstract:

Aiming at a class of cooperative control problems for multi-agent systems with hysteresis inputs， an asymptotic control compensation algorithm of neural network finite-time performance based on a dynamic surface was designed. Firstly， Funnel control was combined with a finite-time performance function to ensure that the consensus error could enter a predefined range in finite time. Second， the unfavorable effects of unknown nonlinear functions within the system and unknown external perturbations were eliminated using Radial Basis Function Neural Network （RBFNN） as well as inequality transformations. In addition， by estimating the upper bounds of some unknown variables， the number of adaptive laws required in the design process was greatly reduced. At the same time， a nonlinear filter with hyperbolic tangent function was proposed to avoid the problem of “differential explosion” in the traditional backstepping control， and eliminate the filter error. Finally， a hysteresis pseudo-inverse compensation signal was designed based on the proposed nonlinear filter to effectively compensate the unknown hysteresis without constructing the hysteresis inverse. Using the Lyapunov stability theory， it is verified that all signals within the closed-loop system are bounded and the consensus error converges to zero asymptotically. Simulation examples also show the effectiveness of the proposed algorithm.

Key words: unknown hysteresis, Radial Basis Function Neural Network (RBFNN), dynamic surface, finite-time Funnel control, pseudo-inverse compensation, Multi-Agent System (MAS)

摘要：

针对一类具有磁滞输入的多智能体系统协同控制问题，设计一种基于动态面的神经网络有限时间性能渐近控制补偿算法。首先，通过Funnel控制结合有限时间性能函数，确保一致性误差可以在有限时间内进入预定义范围。其次，使用径向基函数神经网络（RBFNN）和不等式变换消除系统内未知非线性函数和未知外部扰动带来的不利影响。此外，通过估计一些未知变量的上界，大幅减少设计过程中所需自适应律数；同时，提出一种具有双曲正切函数的非线性滤波器，避免传统反步控制中的“微分爆炸”问题，并消除滤波器误差。最后，基于所提非线性滤波器设计一种磁滞伪逆补偿信号，在不需要构建磁滞逆的情况下有效补偿未知磁滞。利用李雅普诺夫稳定性理论，验证了闭环系统内所有信号都有界，一致性误差渐近收敛至零。仿真实例也表明了所提算法的有效性。

关键词: 未知磁滞, 径向基函数神经网络, 动态面, 有限时间Funnel控制, 伪逆补偿, 多智能体系统