Research On Distributed Controls For Triangular Nonlinear Multi-agent And Large-scale Systems

This dissertation focuses on the design of consensus protocols and distributed con-trols for nonlinear triangular systems.Consensus protocols and distributed controls are for complex systems with multiple subsystems,and contain a series of controllers that can interact via network communication to achieve the overall control objective.On the one hand,the distributed control system provides powerful support and guarantee for large-scale industrial process control.On the other hand,the network communication in the distributed control protocol involves a variety of different topologies such as the di-rected network and the undirected network,which makes traditional control technology difficult to be directly applied.In addition,as the system scale increases,practical sys-tems will inevitably be modeled as multiple nonlinear subsystems.Nonlinear triangular systems are an important class of nonlinear systems,and describe many physical dy-namics.Therefore,for complex systems with subsystems in nonlinear triangular forms,it is of great importance and urgency to design distributed control protocols.This dissertation contains two main parts.The first part is aiming at the case of uncoupling between subsystems(i.e,multi-agent systems),and studies the leader-follower consensus of nonlinear upper-triangular systems under an undirected network,the leader-follower consensus of the uncertain nonlinear upper-triangular multi-agent systems under a directed network,and group consensus of the nonlinear triangular sys-tems under an undirected network.The second part is focusing on the case of coupling between subsystems(i.e.large-scale systems),and constructs the distributed observer for the nonlinear lower-triangular systems and the distributed controller for the nonlin-ear upper-triangular systems.Specifically,the main content of this dissertation can be summarized as below:1.Novel consensus protocols will be developed for a class of upper-triangular nonlinear multi-agent systems under undirected network topologies,where both state feedback case and output feedback case are considered.First,considering the state error between the leader system and follower systems,the consensus problem is trans-formed into a stabilizing problem.Then,the low gain control technique is utilized,and a transformation is introduced on the error state with parameters to be determined.Fi-nally,through estimating the nonlinear terms and analyzing the Laplacian matrix of the undirected network,the parameters are determined,resulting in the consensus protocols(Chapter 2 in the dissertation)2.Novel consensus protocols will be developed for a class of uncertain upper-triangular nonlinear multi-agent systems under directed network topologies,where both state feedback case and output feedback case are considered.The uncertain nonlinear multi-agent systems here can be regarded as the extension of deterministic systems Meanwhile,an undirected network can be considered as a special case of a directed net-work.This dissertation first considers the state error between the leader system and fol-lower systems,which converts the consensus problem into a regulating problem.Then by adapting the dynamic low gain control technology,a new state is obtained by combin-ing the error state with a time-varying parameter.Finally,according to the comparison theorem of differential equations,the time-varying parameter is designed.Therefore,the corresponding consensus protocol is achieved.(Chapter 3 in the dissertation)3.Novel group consensus protocols will be developed for a class of heterogeneous triangular nonlinear multi-agent systems under directed network topologies.The multi-agent system incorporates two leader systems to describe two different mathematical models.First,by designing a two-layer distributed observer,each controller can con-struct the states of the two leader systems.Then,the dynamics of each subsystem are identified to determine the dynamic structure of the followers.Finally,based on the identified information,the group consensus protocol of the nonlinear triangular system is further designed,so that each follower tends to be consensus with the leader which has the same models.(Chapter 4 in the dissertation)4.A novel distributed observer will be designed for a class of large-scale lower-triangular nonlinear systems under directed network topologies.The nonlinear lower-triangular system here is formed by multiple subsystems coupling with each other,which results in the output information of each subsystem cannot be employed to re-construct all or even part of the system states.Distributed observers consider multi-ple communicating sub-observers that work together to estimate the system dynamics.Here,each observer can not only interact with some other observers,but also obtain some output information from the original system.This dissertation first considers the state error between the system and sub-observers,and transforms the designing problem of distributed observers into a stabilizing problem.Then,a time-varying state trans-formation is introduced into the error state and the Lyapunov function is constructed.Finally,through analyzing the Laplacian matrix of the network topology,the Cauchy-Schwarz inequality is employed to achieve the distributed observer.(Chapter 5 in the dissertation)5.A novel distributed control approach will be developed for a class of large-scale upper-triangular nonlinear systems under directed network topologies.This disserta-tion considers that each controller for the subsystem only depends on its own output information,and its control gain will be adjusted through the network.First,for each subsystem,a controller with undetermined parameters is presented,and through esti-mating the nonlinear terms,the stable conditions of the system are obtained for the parameters.Then,the parameters are designed based on the neighbour dynamics,so that the subsystem controller needs to not only deal with its own nonlinear coupling,but also adjust its dynamics responding to the nonlinear coupling between subsystems.Finally,according to the stability conditions and the dynamic adjustment of the param-eters,it is ensured that the distributed control can effectively stabilize the large-scale nonlinear upper-triangular systems.(Chapter 6 in the dissertation)In summary,this dissertation designs a series of distributed control algorithms through the research of triangular nonlinear multi-agent systems and large-scale trian-gular nonlinear systems.Its main contributions can be summarized as follows:1.the distributed low-gain feedback control technology for upper-triangular nonlinear systems is introduced,which promotes the consensus-related researches on the upper-triangular nonlinear multi-agent systems;2.the distributed pre-specific time control technology for the lower-triangular nonlinear system is built,which provides a novel technology to estimate the system state;3.a distributed control strategy is proposed,which enables to design a distributed control for strong coupling systems and provides new research ideas for the study of stabilization and control of large-scale nonlinear systems.