Strict consensus is difficult to be implemented due to the stochastic behavior of multi-agent systems (MASs), so a new concept, distribution consensus, is proposed here to keep the agents’ consensus in the stochastic sense, i.e., the output errors do not converge to a fixed value but follow a desired distribution function. The appropriate control protocol, with the output error probability density function (PDF) as the target, is designed based on the combination of sliding mode control and PDF compensation. Sliding mode control is the core part to ensure the whole system’s stability, and the PDF compensator is used to compensate the random variation and reduce the chattering effect, respectively. In order to realize the complete control in real time, the PDF compensator is modeling by a radial basis function (RBF) neural network and its optimal control law is calculated by the iterative training of RBF network weights. Finally, the effectiveness of the proposed method is verified by MASs simulations with three different communication topologies. The PDF compensator can greatly improve the consensus effect for the nonlinear stochastic MASs.

由于多智能体系统（MAS）的随机行为，很难实现严格的共识，因此在此提出了一个新的概念，即分布共识，以保持代理的共识在随机意义上，即输出错误不会收敛到固定值，但遵循所需的分布函数。基于滑模控制和PDF补偿的组合，设计了以输出错误概率密度函数（PDF）为目标的适当控制协议。滑模控制是确保整个系统稳定性的核心部分，而PDF补偿器则分别用于补偿随机变化并降低抖动效果。为了实现实时的完全控制，PDF补偿器是通过径向基函数（RBF）神经网络建模的，其最佳控制律是通过RBF网络权重的迭代训练来计算的。最后，通过三种不同通信拓扑的MAS仿真验证了该方法的有效性。PDF补偿器可以大大提高非线性随机MAS的共识效果。