This paper investigates the optimal synchronisation problem for unknown nonlinear heterogeneous multi-agent systems (MASs) with an active leader and disturbances. Due to the external input signal of the active leader, the resulted uncooperative behaviours and unpredictability increase difficulty to derive the analytical solution of the coupled Bellman equation. To this end, we develop a distributed model reference adaptive critic learning algorithm with a hierarchical and distributed synchronisation control framework, which transforms the synchronisation problem of unknown nonlinear MASs into that of defined reference ones. Moreover, the algorithm extends our previous work to the distributed MASs, so that it is guaranteed that all the agents reach an agreement with the minimised transient errors and robustness against the disturbances and the neural network (NN) approximation errors. It is proved that the local neighbour tracking errors and the NN weight estimation errors are uniformly ultimately bounded via Lyapunov stability theory. A simulation example for multi-manipulator systems demonstrates the effectiveness of the algorithm.

本文研究了具有主动领导者和干扰的未知非线性异构多智能体系统 (MAS) 的最优同步问题。由于主动领导者的外部输入信号，导致的不合作行为和不可预测性增加了求解耦合贝尔曼方程解析解的难度。为此，我们开发了一种分布式模型参考自适应批评学习算法，该算法具有分层和分布式同步控制框架，将未知非线性 MAS 的同步问题转化为已定义参考 MAS 的同步问题。此外，该算法将我们之前的工作扩展到分布式 MAS，从而保证所有代理都与最小化的瞬态误差和对干扰和神经网络 (NN) 近似误差的鲁棒性达成一致。通过李雅普诺夫稳定性理论证明了局部邻居跟踪误差和NN权重估计误差最终一致有界。一个多机械手系统的仿真例子证明了该算法的有效性。