Event‐triggered gradient‐based distributed optimisation for multi‐agent systems with state consensus constraint

Abstract

This study focuses on the event-triggered gradient-based algorithm for a distributed optimisation problem of multi-agent system subject to state consensus constraint over directed networks, where each agent has local access to its own strongly convex utility function. A novel gradient-based optimisation consensus algorithm is proposed to solve the optimisation consensus problem, where the event-triggered strategy based on sample-data is employed. In contrast to previous optimisation consensus work, their algorithm guarantees that the equilibrium point of the multi-agent systems is optimal solution, and it uses the constant step-size in the optimisation term. Under the algorithm, it can be proved that there exists a certain vector established with the optimal solution is the system equilibrium point and also the consensus point. Moreover, the sufficient condition on optimisation consensus for multi-agent systems is derived. Finally, a numerical simulation example is given to illustrate the theoretical analysis.