Identification,Estimation And Control Of Complex Dynamical Networks

Recently,network science has been a focus issue for reaserchers from various fileds owing to the wide application of complex dynamical networks in mathematics,physical mechanics,management science,computer science,social science and biology,etc.In comlex dynamical networks,the interconnection of nodes leads to complex collective dynamic behaviors.Toplogy identification and state estimation are prerequisites for predicting and controlling the collective behaviors.As special complex dynamical networks,the consensus problem is the basic reaserch of multi-agent systems.This thesis,based on the observer theory,adaptive control and sampled control theory,investigates the topology identification problem and state estimation problem for complex dynamic networks,and explores the consensus tracking problem for multi-agent systems.The main contents are as follows.For the complex spatio-temporal networks with coupling time delay,the topology identification problem is investigated based on the adaptive observer method.Most existing topology identification methods have been studied on the complex networks modelled by ordinary differential equations.However,many realistic complex networks are spatio-temporal whose dynamics depend on not only time but also spatial position.This kind of neworks should be described by partial differential equations,which brings difficulty to topology identification.Firstly,the observer network is constructed for the complex network with unknown topology.For the feedback control gain and topology estimator,adaptive updating laws in integral form are designed.Secondly,according to theoretical analysis,the observer network would be driven to synchronize with the network with unknown topology.At the synchronization time,the unknown topology can be identified by the topology estimator.Finally,the relationship between the topology identification speed and the parameters in the adaptive laws is analysed by the numerical simulation.For the complex spatio-temporal networks with non-differentiable coupling time delay,the finite-time topology identification problem is investigated based on the auxiliary system method.Firstly,by constructing the auxiliary system,a relationship between the unknown topology vector and two measurable matrix signals is developed.Secondly,two finite-time topology identification methods are proposed based on the obtained relationship.One method of identifying the topology in finite time is to solve the equation through computing invertibility of the matrix.Besides this method,an adaptive law is developed to infer the topology online in finite time while avoid computing the invertibility of the matrix.The proposed two methods do not require the differentiability of the time-varying coupling delay which relaxes the assumption of the time delay.Finally,the topology identification methods are also developed for complex spatiotemporal networks with unknown system parameters.For the complex networks with nonlinear coupled function,the state estimation problem is addressed based on the sampled measurements of partial nodes.The hybrid distributed sampled observer is designed based on the partial control.In order to recover the output data during the sampled interval,the output predictor is introduced.The feedback control of the observer is updating with time in the sampling interval by employing the output predictor.The state estimation only requires sampled output data of partial nodes by employing the partial control,which saves the measurement cost.According to the Lyapunov stability analysis,sufficient conditions are established to assure the distributed observer is an exponential observer for the original network.For the uncertain multi-agent systems with time-varying state delay,the consensus tracking problem is studied based on the leader's sampled data.A distributed sampled observer with hybrid form is proposed to estimate the leader' state.Based on the observer,adaptive tracking control is designed for each agent.An auxiliary term is added in the control to eliminate the influence of the estimation error produced by the parameter estimator.By choosing appropriate auxiliary function,the parameter estimation error and time-varying state delay can be separated from the tracking error system.It simplifies the tracking error system and relaxes the differentialbility of the time-varying delay which is commly used.Based on the linear matrix inequality method and Lyapunov stability theory,sufficient conditions are established to guarantee that the consensus tracking error and the parameter estimation error exponentially converge to zero.For the high-order uncertain multi-agent systems,the adaptive dynamical surface tracking control is studied based on the leader's sampled data.The dynamic surface control is introduced to solve the “explosion of complexity” caused by the traditional backstepping method for high order system.By employing the backstepping method and dynamic surface control,the adaptive control input is designed based on the hybrid distributed sampled observer.In virtual control at each step,a compensation term is added to improve the convergence speed of the error terms.According to the theoretical analysis,some sufficient conditions are obtained to assure that the close-loop system is semiglobally uniformly ultimately bounded,and the tracking error and the parameter estimation error converge to a sufficiently small neighborhood around origin.