A Fixed-Time Distributed Optimization Algorithm Based on Event-Triggered Strategy

This paper considers the fixed-time distributed optimization problem with consensus constraint and strongly convex local cost functions, and a distributed optimization algorithm involving two stages is designed. The first stage is to make each agent converge to its own locally optimal state (the minimizer of local cost function) from any initial value in fixed time by designing distributed local optimization controllers. The second one is to realize the goal that all agents achieve the globally optimal state (the minimizer of global cost function) in fixed time under the distributed global optimization protocol. During the second stage of the proposed algorithm, each agent only communicates with its neighbors at event-triggered instants. Hence, comparing to the continuous communication optimization algorithm, our method has the advantage in the terms of saving the communication resources. Furthermore, Zeno behavior is avoided under such control strategy. The proposed algorithm in this paper can ensure that all agents achieve the globally optimal state in fixed time, which is independent of agents' initial values and decided by some tunable parameters. Finally, the effectiveness of the presented optimization algorithm is demonstrated by a simulation example.