Research On Distributed Consensus And Optimization Under Limited Communication Resources

Inspired by some magical phenomena of nature,e.g.,bird flock can maintain a certain formation during flying,fishes in a fish school can swim at the same speed,the socalled multi-agent network has been attracting considerable attentions in recent decades.A multi-agent network usually consists of many individual agents that own perception,computation,and communication abilities.Instead of undertaking different tasks separately,each individual agent communicates with its neighbors and then achieves a global goal cooperatively together with other agents.Multi-agent network has significant advantages in handling large-scale complex systems for its convenience,high efficiency,and robustness.It is now widely applied in many kinds of fields and disciplines,such as UAV formation control,multi-area power systems,etc.To tackle with the common existing constraint in multi-agent networks,namely the limited communication resources,in this work,we consider the distributed consensus and optimization problems in multi-agent networks with limited communication energy supply and limited communication bandwidth.In order to reduce the waste of communication energy supply and bandwidth as much as possible,we introduce the so-called event-triggered control and quantized control to the distributed consensus and optimization algorithms design.The main contributions can be summarized as follows.1.For the distributed consensus,we propose a event-triggered quantized communication based framework for the algorithm design.In this framework,the event-triggered mechanism and quantized mechanism are provided explicitly.Also,in order to compensate the effect brought by mismatched disturbances,we also propose a novel multiple discontinuous sliding mode surface and the corresponding sliding mode control law is constructed by considering the sliding mode surface with the event-triggered and quantized mechanisms jointly.Under such a scheme,it is shown that the state trajectories of all the agents will be regulated to achieve consensus asymptotically and the Zeno behavior can be avoided completely.For the distributed optimization,we follow the previous work in the distributed consensus part to construct a consensus-based distributed optimization algorithm.We prove that the proposed distributed optimization algorithm can drive the states of all the agents to the local optimum in the constrained set asymptotically with the Zeno behavior being excluded.2.We further extend the proposed algorithms to self-triggered and periodic eventtriggered cases.Particularly,in periodic event-triggered approach,the systematical method of redesigning the triggering conditions and the upper bound of sampling periods are provided explicitly.As a result,all the agents can reach bounded consensus for the consensus part and all the agents can be regulated to a small stable region contains the local optimum in the constrained set for the optimization part.Moreover,the upper bound of the consensus error(stable error between states and the local optimum)can be adjusted by appropriately selecting parameters and the periodic event-triggered case will be reduced to the event-triggered case when the bound approaches to 0(sampling periods approach to 0 at the same time).Finally,we give the conclusion of this thesis and some remarks on future works are discussed.