Distributed adaptive consensus control of heterogeneous multi-agent chaotic systems with unknown time delays

In this study, the distributed consensus tracking problem for heterogeneous multi-agent chaotic delayed non-linear systems is addressed. Each follower is modelled as a chaotic system with non-identical and unknown time delays, non-linear dynamics, and disturbances. The general case of directed communication graphs is considered and the graph structure is taken into account in the control protocol design. Distributed controllers with an adaptive learning feature based on neural network approximations are designed to guarantee that all agents synchronise to the leader´s state with bounded synchronisation error. A graph-dependent Lyapunov proof provides error bounds that depend on the maximum time delays, the graph topology, and the agent dynamics properties. Special cases of the dynamics considered here cover many examples in the literature, including master-slave synchronisation of two chaotic delayed systems. A simulation with multiple non-identical chaotic agents is given to verify the effectiveness of the proposed method.