Multi-Objective Event-triggered Consensus of Linear Multi-agent Systems

This paper proposes a distributed consensus algorithm for linear event-based heterogeneous multi-agent systems (MAS). The proposed scheme is event-triggered in the sense that an agent selectively transmits its information within its local neighbourhood based on a directed network topology under the fulfillment of certain conditions. Using the Lyapunov stability theorem, the system constraints and event-triggering condition are expressed in terms of several linear matrix inequalities (LMIs) to derive the consensus parameters. The objective is to design the transmission threshold and minimum-norm heterogeneous control gains which collectively ensure an exponential consensus convergence rate for the closed-loop systems. The LMI computed control gains are robust to uncertainty with some deviation from their nominal values allowed. The practicability of the proposed event-based framework is further studied by proving the Zeno behaviour exclusion. Numerical simulations quantify the advantages of our event-triggered consensus approach in second-order, linear and heterogeneous multi-agent systems.