Distributed Adaptive Control Of Uncertain Network Systems

Distributed control theory of network systems is a product of the era of internet,and has been widely used in several fields spanning from intelligent transport,smart grid,industrial internet,and so on.By treating the subsystems(agents)in a network system as nodes and treating the communications between different subsystems as edges,the control theory of network systems can be simply understood as the control theory over graphs.distributed control methods usually take good advantage of the communication mechanisms between subsystems so as to achieve the control goal.Thus,they usually enjoy the properties of high parallelism,powerful scalability,privacy protection,etc.On the other hand,as an important branch of control theory and applications of uncertain systems,adaptive control refers to the strategy of incorporating self-tune mechanisms in the controller,endowing the controller with certain adaptive capability to the system un-certainties.Considering that there are duplex uncertainties in both individual behaviors and global interactions in realistic network systems,the theory of distributed adaptive control has important research value and application prospect.This thesis starts with distributed adaptive control problems including consensus,tracking,containment,and formation,of several classes of network system with uncertainties in individual behav-iors and/or global interactions.Then,from a control perspective,distributed adaptive optimization and resource allocation algorithms are proposed for network systems with structural uncertainties.The main results of this thesis are summarized as follows:(1)The study of distributed adaptive control methods for consensus,tracking and containment.Firstly,a class of network systems with unmodeled dynamics and unknown disturbances,and neural network based fully distributed adaptive control method is pro-posed for all leaderless consensus,consensus tracking with a single leader,and contain-ment with multiple leaders.By introducing adaptive neural networks,adaptive coupling gains,and nonsmooth techniques simultaneously,the proposed method requires neither the algebraic connectivity of the global network,nor the upper bounds of the leader-s' inputs or the disturbances.Secondly,an average tracking of external time-varying signals for network systems with unmodeled dynamics is studied,and feedback designs with both static coupling strategy and dynamic coupling strategy are proposed,respec-tively,where the latter relaxes the dependence on the global information to some degree.Finally,a tracking problem with multiple uncertainties(unmodeled dynamics,unknown disturbances,time-delay,high-dimensional leader)is considered,and a control strategy with bounded tracking errors is proposed by designing distributed observers and neural network based feedback compensations.(2)The study of distributed adaptive control methods for formation.First,a class of uncertain network systems is considered with unmodeled dynamics communicating over an undirected graph,and two classes of distributed neural network adaptive time-varying formation methods are proposed.Dynamic coupling feedback designs are ana-lyzed from node and edge viewpoints,respectively,where the node-based design is fully distributed without any global information,while the edge-based design is applicable to the network system with switching communication topologies.Then,for network systems over directed graphs,a(generalized)directed-spanning-tree based time-varying formation(tracking)control solution is provide(in the presence of one or leaders).The proposed solution effectively solves the distributed adaptive formation control over a directed network without the knowledge of the generalized algebraic connectivity.(3)The study of distributed adaptive control methods for optimization and resource allocation.Considered first is the distributed optimization problem over strongly con-nected digraphs.A novel framework based on a directed-spanning-tree is proposed for continuous-time distributed adaptive optimization:a distributed adaptive optimization algorithm is proposed for weight-balanced digraphs,and a finite time weight-balancing al-gorithm is proposed for weight-unbalanced digraphs,both based on a directed-spanning-tree.The proposed framework requires neither convexity of local function,nor vanishing step sizes,nor algebraic information(eigenvalues or eigenvectors)of the Laplacian ma-trix.Next,we consider a distributed optimization problem with global constraints,i.e.,resource allocation.Starting from an uncertain saddle-point dynamics,two classes of distributed adaptive resource allocation algorithms are proposed based on the directed-spanning-tree and the nodes,respectively.Under reasonable assumptions,the proposed algorithms both realize the adaptive resource allocation when the information of the global Laplacian eigenvalues is not available.