Event-Triggered Optimal Consensus of Second-Order MASs with Disturbances and Cyber Attacks on Communications Edges

This paper investigates the distributed optimal consensus problem (DOCP) for second-order multi-agent systems (MASs) in the presence of system disturbances and cyber attacks on communication edges. In optimization, the global objective function is the sum of a class of local private objective functions, which are assumed to be strongly convex and continuously differentiable with Lipschitz continuous gradients. Unlike most optimization problems for MASs studied in the literature, in this study, the dynamics of agents are second-order and disturbed, considering cyber attacks among neighboring agents. In order to achieve DOC with low online resource consumption, novel distributed event-triggered controllers are designed for agents. Not only the communication and computation resources can be saved, but also the frequency of controller updates can be reduced. Moreover, the controllers can prevent the information of the states of second-order MASs from leaking to neighbors. Under restrictions on cyber attacks, sufficient conditions are derived, under which all controlled agents can achieve consensus on the optimal solution of the global objective function exponentially. Furthermore, the Zeno-behavior is excluded on triggering time sequences. Finally, three simulation examples are shown to illustrate the effectiveness of the designed controllers in saving online resources.