Research On Event-Triggered Distributed Optimization Algorithms

In the era of networking,more and more engineering problems are presented in the frame of network systems and can be modeled as distributed optimization problems under multi-agent networks.In network systems,each node acts as an agent and has a local objective function,and the global objective function is the sum of the local objective functions.The purpose of distributed optimization is to design algorithms to find the optimal solution of the whole network optimization problem via cooperation among multiagents.In particular,event-triggered strategies play a very important role in saving resources and reducing communication costs.Therefore,this thesis focuses on the problem of the event-triggered distributed optimization algorithms as follows.Firstly,a distributed event-triggered PID algorithm is studied.A continuous-time PID optimization algorithm is designed in this thesis under the case of undirected connected graphs using only local information of the agents.Under the condition that the global objective function is strictly convex,the global exponential convergence of this continuoustime algorithm is proved using matrix transformation and inequality techniques.After that,an event-triggered PID distributed optimization algorithm is designed to reduce the communication resource consumption.It is demonstrated that the algorithm not only converges globally exponentially to the optimal solution,but also that there is no Zenobehavior in the event-triggered time sequence.Moreover,the effectiveness of the algorithm is verified with a numerical example.Secondly,an event-triggered distributed resource allocation optimization problem is studied.For the second-order multi-agent system,this thesis designs a continuous-time distributed resource allocation optimization algorithm.Under the condition that the global objective function is strictly convex,the global exponential convergence of the algorithm is proved by matrix transformation and inequality techniques.After that,an event-triggered distributed resource allocation optimization algorithm is designed to save communication costs.It is proved that the algorithm not only converges globally exponentially to the optimal solution,but also there is no Zeno-behavior in the event-triggering time sequence.Moreover,a numerical simulation tests the established theoretical results.