Research On Dissipativeness Of Large-scale Networked System

Large-scale networked systems can be considered to be composed of many subsystems with different(or the same)dynamic characteristics interconnected according to a certain network topology.Generally,subsystems communicate with other subsystems in a simple and predictable way,but when the system is regarded as a whole,it has complex and rich dynamic behaviors.With the development of communication and computer technology,the system scale is becoming larger and larger,and many research topics are facing great challenges,including dissipative analysis.Dissipativity is a more general index than stability,passivity,and H_∞performance.Using the traditional method based on lumped description to study the dissipativity of large-scale systems will inevitably bring computational difficulties.Therefore,how to obtain more computationally efficient dissipativity criteria and ensure the dissipativity of the closed-loop system through the design of distributed controllers is one of the important topics in the research of large-scale networked systems.This thesis mainly includes the following contents.Firstly,this thesis investigates the dissipativity analysis of large-scale networked systems with linear time-invariant dynamics.The networked system is composed of a large number of subsystems whose connections are arbitrary,and each subsystem can have different dynamics.A sufficient and necessary condition for the strict dissipativity analysis of the networked system is derived,which takes advantage of the block-diagonal structure of the system parameter matrix and the sparseness characteristics of the subsystem interconnections.Compared with the traditional lumped condition,this condition does not introduce additional conservatism,and the computational efficiency can be significantly improved by sparse solver.Then,a necessary condition and a sufficient condition that depend only on a single subsystem parameter are given separately,which have higher computational efficiency in the dissipative analysis of large-scale networked systems.Secondly,the(Q,S,R)-dissipativity of large-scale networked systems in discrete time is studied.When Q,S,and R take appropriate matrices,the(Q,S,R)-dissipativity of networked systems can be transformed into H_∞performance and strict passivity,respectively.When the number of subsystems is large,the traditional analysis method based on lumped description may have computational difficulties.Some computationally attractive conditions are derived,and their relationship with existing conditions is discussed.Numerical simulations illustrate that compared with the existing results,the conditions suggested in this thesis have higher computational efficiency in the dissipative analysis of large-scale networked systems.Thirdly,based on the dissipative analysis,the design of distributed controllers is considered to ensure the dissipativity of large-scale networked systems.Due to the spatial distributed characteristics of large-scale systems,distributed controllers combine the advantages of lumped controllers and decentralized controllers,which can generally make the closed-loop system achieve better overall system performance.Firstly,we give a sufficient condition to test the dissipativity of the corresponding closed-loop system,which only depends on the parameters of a single subsystem.Then,the existing condition of distributed controller and the solution method of controller parameters are given,so that the obtained controller can guarantee the strict dissipativity of the corresponding closed-loop system.In the end,numerical examples are given to verify the effectiveness of this method.