Research On Multi-Agent Systems Synchronization Problem Under Switching Topologies

The research on complete consensus of networked multi-agent systems with the aim to reach an agreement have been widely conducted in recent years.However,in many cases,the states of the coupled systems may not always synchronize to the same trajectory.A real-world complex network can be divided into some smaller subnet-works.This phenomenon can be observed when systems synchronize to several differ-ent groups,which in the following are termed clusters.So far,the cluster synchroniza-tion phenomenon has attracted the researchers from various disciplines of engineering and science.According to our survey,most researches are focus on the consensus prob-lem on fixed topology.Therefor our thesis mainly deal with the consensus problem under switching topology with distributed controller.Our main innovations are:(1)ro-bust cluster synchronization in dynamical networks with directed switching topology.(2)output synchronization for heterogeneous system.(3)distributed optimization prob-lem with adversarial agents over Markov switching topology.The main contribution of this thesis can be summarized in the following:1.We investigate the bounded cluster synchronization problem of dynamical sys-tems,which can be of generic linear type or Lipschitz nonlinear type,over di-rected switching network.Each cluster is equipped with a virtual leader which produces the desired trajectory for the agents to track.It is required only a frac-tion of systems are influenced by the leader.The interaction topology,which describes the information exchange among the dynamical systems as well as the virtual leaders,is allowed to be time-varying with a well-defined average over an infinite horizon.That is,each augmented cluster,consisting of the agents as well as the corresponding virtual leader,in the time-average network topology is required to have a directed spanning tree.We then transform the cluster syn-chronization problem into a stability problem via averaging method.It is proved that the convergence property for both types of dynamical systems is exclusively determined by the averaging system if the network topology switches sufficiently fast compared to original systems.Finally,it is concluded that if the intra-cluster coupling strength of the time-average topology is stronger than a threshold,then bounded cluster synchronization can be realized for fast switching linear or non-linear systems.2.We employ contraction theory to solve cluster synchronization problem under directed topology.According to the cluster structure,we develop an invariant subspace.Then we take the advantage of the complementary space to prove that the whole systems will synchronize to this invariant subspace,leading to cluster synchronization.We first deal with the linear systems which are linearly coupled under the framework of directed topology.Some sufficient conditions are given to guarantee that the coupled linear systems can achieve cluster synchronization.Moreover,the case of linearly coupled non-linear systems is also considered.3.Output consensus for a series of heterogeneous systems under Semi-Markov switching topology is investigated.The scenario under consideration is that none of the graph is assumed to be connected and the mode-switching delay is ex-isted.The main technical challenge is model and controller dismatch because of time delay.Assuming every individual system is stabilizable and detectable and mild connectivity assumption on communication topology,the coupled sys-tem without model-switching delay can achieve output synchronization by using the Lyapunov method.For the coupled systems with model-switching delay,a bounded output synchronization conclusion can be given.The existence of con-troller design is also investigated.By the way,we prove an exponentially stable stochastic system,in mean square,with non-vanishing perturbation can achieve uniform boundedness and ultimate boundedness.4.We investigates the distributed optimization problem with adversarial agents over Markov switching topology.A Push-DIGing algorithm is proposed to seek the optimal solution to the distributed optimization problem.Different from most existing thesis about distributed optimization problem with adversary agents,we mainly focus on fixed step size to deal with the distributed optimization problem under Markov switching communication topology.We first divide the agents into three sets:the trust agent set,the normal agent set and the adversarial agent set.All normal agents only use the state of non-attacked agents for iterations.A practical method is presented to distinguish the adversary agents.It is shown that the trust agents and normal agents will synchronization to the optimal value in a bounded error if the step-size does not exceed the upper bound;the union graph of the switching topology has a spanning tree and the differential of local function is decreasing.Furthermore,we also present the upper and lower distance between the final trajectories and the optimal trajectory.