Analysis And Synthesis In Multi-Agent Systems With Complex Network Structure

Consensus/synchronization is a trans-disciplinary concept and has a long history,arising in biology,engineering,social science and so on.It refers to the scenario that agreement is reached for a certain quantity of interest,such as position and velocity.Typical examples include distributed optimization with consensus constraint.In the past decade,consensus/synchronization has drawn dramatic attention in the field of systems and control for multi-agent systems.This is inspired by its applications in formation control and attitude alignment.Despite the fruitful and insightful results that made by various researchers,many open problems still exist.In this thesis,we focus on two of them.One is cluster consensus/group synchronization when the multi-agent system is divided into several clusters of heterogeneous nodes,and each cluster is controlled to reach consensus/synchronization.The other one is synchronization of high-order multi-agent system over dynamic networks,which is fascinating and challenging.The following contributions are made.1)In Chapters 3 and 4,we deal with the consensus problem of multiple partialstate coupled linear sy stems that are neutrally stable.These sy stems communicate over dynamic undirected networks which change continuously or piecewise fixed but can be disconnected at any time.We develop an analysis framework from uniform complete observability theory to work out the necessary and sufficient condition for exponential consensus.We figure out the proof by using matrix analysis and linear functional analysis.It turns out that exponential consensus can be realized globally and uniformly if and only if a joint(?,T)-connectivity condition and an observability condition relying only on system and input matrices are satisfied.2)In Chapter 5,we address the output containment control problem for a network of heterogeneous linear multi-agent systems.The control target is to drive the outputs of the followers into the convex hull spanned by the leaders.To this end,we first derive a necessary condition imposed on both system dynamics and network topology from the viewpoint of internal model principle.Then,we utilize a dynamic controller to drive the outputs of the leaders and followers to track the reference trajectories to achieve containment exponentially.Both fixed and dynamic network topology are taken into consideration.Then,an optimal control law is constructed from an algebraic Riccati equation,which is proved to be a stabilizing one as well.Finally,a reinforcement learning algorithm is introduced to solve the optimal control problem online without the knowledge drift dynamics.3)In Chapter 6,we investigate group synchronization for multiple interacting clusters of non-identical systems.By observing the structure of the coupling topology,a Lyapunov function based approach is proposed to deal with linear systems which are linearly coupled in directed topology.Such an analysis is then extended to tackle the case of nonlinear systems in a similar framework.Moreover,the case of nonlinear systems which are nonlinearly coupled is also addressed,however,in the undirected coupling topology.For all these cases,a consistent conclusion is made that group syn-chronization can be achieved if the coupling topology for each cluster satisfies certain connectivity condition and further,the intra-cluster coupling strengths are sufficiently strong.Both the lower bound for the intra-cluster coupling strength as well as the convergence rate are explicitly specified.4)In Chapter 7,we deal the output group synchronization for a network of heterogeneous linear systems such that the outputs of the nodes synchronize with each other in every cl u ster.Two different setups in terms of availability of the states of the reference generators are taken into consideration.A unified approach inspired by the internal model principle is proposed.First,coupled reference generators are constructed to produce synchronized reference traj ectories.Second,feedback controllers are designed to steer the output of each node to its corresponding reference trajectory.The two setups differ from each other in that the coupling configuration for reference generators and design of feedback controllers are rather different.Specifically,when the states of the reference generators are not available,the small gain theorem is exploited to drive the outputs of the nodes to the synchronized ones of virtual reference generators.5)In Chapter 8,we focus on the H? group consensus for networks of agents modeled by single-integrator with model uncertainty and external disturbance.By developing tools from algebraic graph theory,matrix analysis as well as Lyapunov stability theory,we are able to derive some sufficient conditions in terms of the structure and strength of the couplings among agents to guarantee the group consensus with desired H? performance.Furthermore,some adaptation laws are proposed to address the coupling strength problem ari sing from the consideration that the theoretical value is usually much larger than expected in practice.