Control And State Estimation For Complex Dynamic Network

A complex dynamic network is a kind of network consisting of a large number of coupled nodes,which can be used to characterize the interconnected complex systems in nature,human society,and engineering fields.Due to the large number of nodes and complicated connections between the nodes,complex dynamic networks exhibit rich dynamical behaviors.An in-depth study of the dynamical behavior of complex dynamic networks can help to understand the principles of population behavior and explore the operating mechanism of complex systems.In practical applications,due to the limitation of network bandwidth and network equipment performance,the transmission information is inevitably affected by network-induced phenomena,such as transmission time delay,data quantization,network congest,network attacks,and so on.In addition,the limitations of physical devices and the unknown model of the controlled objects are pretty ubiquitous in dynamic complex dynamic networks,which presents a series of challenging new topics for the study of control and state estimation problems in complex dynamic networks.In this thesis,we focus on the control and state estimation for several complex networks.The dynamic networks under consideration are involved with distributed time delay,dynamic quantization,input saturation,cyber attacks,partial node measurement output availability and unknown system model.With the help of Lyapunov stability theory,modern control theory,algebraic graph theory,switching system methods and linear matrix inequality techniques,we are devoted to several hot topics concerning the control and state estimation of complex dynamic networks.The research contents of this thesis are summarized as follows:(1)The sampled-based consensus problem is investigated for a class of nonlinear multi-agent networks with bounded distributed time-delays and quantisation effects.Compared with the static quantization method,some adjustable parameters are introduced to design the dynamic quantization strategy,which can dynamically adjust the quantization level to avoid the quantizer saturation phenomenon.In addition,to reduce the actuation burden of controller and cost of quantiser,a sampling control mechanism is applied to design a consistent protocol for multi-agent networks.By constructing a new Lyapunov-Krasovskii functional,and applying algebraic graph theory and inequality techniques,several sufficient criteria are derived to achieve consensus of multi-agent systems.On this basis,the controller gain matrix can be computed by solving a set of linear matrix inequalities.(2)The sampled-data bipartite tracking consensus problem is investigated for a class of nonlinear multi-agent networks subjected to input saturation.Both competitive and cooperative interactions coexist among agents in the concerned network.By resorting to Lyapunov stable theory and linear matrix inequality technique,several criteria are obtained to ensure that the considered multi-agent networks can achieve the bipartite tracking consensus.Besides,with the help of the decoupled method,the dimensions of linear matrix inequalities are reduced for mitigation of the computation complexity so that the obtained results can be applied to largescaled multi-agent networks.Furthermore,the controller gain matrix is explicitly expressed in terms of solutions to a set of linear matrix inequalities.In addition,we provide with an estimate of elliptical attraction domain of bipartite tracking consensus.(3)The sampled-data-based non-fragile bipartite tracking consensus problem is explore for a class of nonlinear multi-agent networks subject to denial-of-service attacks,where each agent communicates with its neighbors over a signed digraph.Due to the existence of malicious attacks,agents cannot receive neighbor information during denial-of-service attacks and the original sampling control system is transformed into aperiodic sampling system.First,we improve the famous Halanay inequality,and by applying algebraic graph theory and Lyapunov stability theorem,derive sufficient conditions for multi-agent networks to achieve bipartite tracking consensus.Especially,when the connection mode between followers is undirected graph,based on the matrix decoupling method,the dimensions of matrix inequalities are reduced for mitigation of the computation complexity so that the obtained results can be applied to large-scaled multi-agent networks.In addition,the controller gain matrix can be explicitly calculated in term of solving a set of linear matrix inequalities.(4)The intermittent dynamic event-based state estimation problem is considered for a class of delayed complex dynamic networks.The estimate is implemented based on the measurements from a fraction of network nodes.In the framework of aperiodic intermittent measurement outputs,a dynamic event-triggered mechanism is introduced to save communication resources and reduce actuation burden.The aim of this work is to design a dynamic event-based state estimator by adopting intermittent dynamic event-triggered strategy,such that the dynamics of estimation error system is exponentially stable.By resorting to Halanay inequality and switched system method,the sufficient conditions are derived for ensuring the existence of the desired state estimator.In the meanwhile,the estimator gains for partial nodes are explicitly obtained by solving some matrix inequalities.Furthermore,it is also proven that Zeno behavior can be excluded under the proposed intermittent dynamic event-triggered strategy.(5)The state estimation problem is studied for a class of switching complex dynamical networks with unknown nonlinear dynamics.Aiming at the unknown nonlinear function,we introduce a neural network to approximate the unknown nonlinear function and construct a novel neural network-based state estimator with non-fragility to fulfill the state estimation task.In order to improve the efficiency of communication resource utilization,an event-triggered mechanism is applied in designing the estimator.By employing the Lyapunov stability theory and inequality technique,sufficient criteria are derived for the existence of the desired exponentially ultimately bounded neural network based state estimator for complex dynamical networks.It is also proven that the proposed event-triggered mechanism can avoid Zeno phenomenon.In addition,the gains of the desired estimators are characterized by the explicit expressions.