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This paper investigates the optimisation problem of second-order multi-agent systems. Distributed optimisation algorithms are proposed based on sampling data. Two kinds of sampling techniques, namely, aperiodic sampling and dynamic event-triggered sampling, are utilised. Moreover, the proportional integral (PI) strategy is utilised in the proposed algorithms. Compared with the existing distributed optimisation algorithm based on periodic sampling, the proposed algorithm dependent on aperiodic sampling is more general. Compared with the existing steady event-triggered algorithm, the distributed optimisation algorithm based on dynamic event-triggered sampling has the merit of lower energy consumption. Under the assumption that the global cost function is strongly convex about global minimum point, it is proved that the proposed algorithms solve the optimisation problem. Lyapunov stability theory is applied to give sufficient criteria guaranteeing convergence to optimal point. Finally, the effectiveness of the proposed algorithms is illustrated by numerical simulation.

Sampling-data-based distributed optimisation of second-order multi-agent systems with PI strategy