Controllability-observability And State Estimation For Complex Dynamical Networks

Nowadays,people live in a world full of various complex networks.The Internet,the communication network,the traffic network,the power grid,the social network,etc,are all closely related to our lives.And the nature world also exists various complex networks such as the food chain network and the neural network.Thus,complex networks get wide attention and researches from many disciplinary fields,e.g.mathematics,biology,system control science and social science,as well as application fields,e.g.energy transmission,communication interconnection,transportation.From the perspective of control discipline,the researches on complex network are mainly concentrated in synchronization and control,state estimation,topology identification,spreading dynamics,etc.In real life,for each network,people often need to know the status information in time,so as to better monitor and regulate the network operation and make correct judgments on the possible network failures and emergencies.However,because the scale of the network is often large,it costs so much to measure the information of all nodes.Meanwhile,affected by practical factors,e.g.bandwidth limit,sensor failure,etc,it is difficult to obtain all the status information of the network.Therefore,it needs to study how to determine the unknown state information from the output information which could be gained directly,i.e.the state estimation problem of the complex dynamical network.The actual process of the network information transmission will be affected by a variety of factors,e.g.noise,time delay,data loss,etc.These unreliable factors will have an impact on the normal network operation,reduce the efficiency of the network transmission,and even cause the serious network failures.Particularly,the data loss problem is common in the real network systems.If the data loss rate is relatively high,it will seriously affect the experience effect of the network applications,reduce the efficiency of various networks and influence the normal production and living.So,aiming at the presence of random data loss,there is a need to find an appropriate compensation method to effectively compensate for the lost data.The constructions of the state observers in most literatures all need to measure the output information of all nodes.However,the practical situation is that not all nodes could be measured to obtain the output information.Thus,how to realize the state estimation while only measuring the output data of partial nodes,is a very meaningful question.Meanwhile,the studies on network controllability and observability provide a new solution to the selection of the measured nodes.Therefore,based on the structural controllability and observability,the state estimation problem of complex dynamical networks with partial measurement is investigated in the dissertation.In this dissertation,considering the random data loss in information transmission channel,the state estimation problem of complex dynamical networks is studied.And an appropriate compensation method is proposed to effectively compensate for the lost data.Meanwhile,the structural controllability and observability problem of complex dynamical networks with multidimensional node dynamics and root Strongly Connected Components that have perfect matching is stuied.Based on the above structural controllability and observability thoughts,the state estimation is realized while only measuring partial node information.The main contributions and innovations of the dissertation are as follows:(1)A state estimation scheme for a discrete-time complex dynamical network with internal and external random data loss is established.Aiming at a complex dynamical network with random data loss happening in the internal and external communication links,a corresponding state estimation scheme is established.In detail,the internal and external random data loss are described as the independent identically distributed Bernoulli random variables,meanwhile,compensated by the state data and the output data of observer,respectively.By applying the Lyapunov stability theory and stochastic analysis method,a sufficient condition for state estimation is derived in the form of linear matrix inequalities(LMIs)to determine the appropriate observer gains,so as to guarantee the observer data finally equal to the lost data and achieve a satisfactory data compensation effect.Through simulation experiments,the data compensation effects with various data loss situations are demonstrated.(2)The structural controllability and observability problem of complex dynamical networks with multidimensional node dynamics is studied.Aiming at the complex dynamical network with multidimensional node dynamics,its structural controllability and observability problem is addressed.By applying the Maximum Matching principle,the minimum driver nodes are obtained.Meanwhile,considering whether the states of driver nodes are completely or partially controlled,the choice problem of the driver states to guarantee the full control on network is studied,and the rigorous criteria are given respectively.By duality,the above results also apply to the structural observability problem of such complex networks.Through simulation experiments,the specific control processes are shown to demonstrate the effectiveness of the complete and partial control of driver nodes.(3)The structural controllability and observability problem of complex dynamical networks with root Strongly Connected Components that have perfect matching is studied.Aiming at a class of complex dynamical networks with root Strongly Connected Components that have perfect matching,its structural controllability and observability problem is studied.First,the multidimensional node is looked as a subnetwork,and the Maximum Matching principle is applied to the network topology to obtain which subnetworks we need to control.Then,an algorithm is proposed to identify a minimum controlled node set of the subnetwork.Finally,by analyzing the structural features of the whole network and synthetically applying the proposed algorithm,Maximum Matching principle and Graphical Approach,a flowchart is designed for identifying the minimum controlled node set of the whole network.By duality,the above results can also apply to the structural observability problem of such complex networks.Through simulation experiments,the specific observation processes are shown to demonstrate the effectiveness of the theoretical results.(4)The state estimation problem of complex dynamical networks with random data loss considering partial measurement is studied.Aiming at a complex dynamical network with random data loss existing on its external communication links to the observers,its state estimation is realized while only measuring the output data of partial nodes,where the lost data are compensated by the corresponding observer data.Depending on whether the network possesses the root Strongly Connected Components that have perfect matching,the choice problem of measured nodes and the construction problem of specific output matrices are discussed.By applying the Lyapunov stability theory and stochastic analysis method,a sufficient condition for state estimation is given.Through simulation experiments,the effectiveness of the proposed state estimation scheme in the independent data loss mode and the synchronous data loss mode are demonstrated respectively.