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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.

Distributed synchronisation control of unknown nonlinear systems with an active leader