Event-triggered distributed optimal coordination of heterogeneous linear MASs over weight-unbalanced digraphs

In this paper, the distributed optimal coordination problem of heterogeneous linear multi-agent systems is studied, in which the actual information of the left eigenvector and out-degree cannot be obtained in advance. The underlying communication network among agents is assumed to be a weight-unbalanced and strongly connected digraph. The global objective function of the whole system is the sum of privately-known local objective functions, which are assumed to be strongly convex with Lipschitz continuous gradients. To achieve the distributed optimal coordination with low communication and computational resource consumption, and to efficiently reduce the frequency of control signal updates, a new distributed event-triggered control scheme is proposed. In this scheme, an auxiliary system with adaptive edge weights is established to generate the optimal trajectories and the tracking control inputs are designed for agents to track the given optimal trajectories. It is privacy-preserving to some extent as no actual state or output information of agents is communicated with neighbors. Sufficient conditions are derived, under which the distributed optimal coordination under consideration can be exponentially achieved. Moreover, the Zeno-behavior is shown to be excluded. Additionally, for cases where agent states are unmeasurable, a new distributed event-triggered observer-based control input is designed for each agent to achieve optimal coordination. Finally, numerical simulations are carried out to show the good performance of the proposed control scheme.