Research On Partial-Nodes-based Information State Estimation For Discrete Complex Networks

The complex networks are composed of a large number of interconnected nodes and edges with specific connection structure.Some dynamic laws of complex networks need to be described by their internal state variables.However,in many actual systems,we could not directly measure the internal state information of the complex networks due to the influence of many factors.Therefore,we can only estimate the whole states of the complex networks with measurable input and output information.Then,we use the estimated states to replace the real states for correlation analysis.Hence,the state estimation problem for complex networks has been an important issue of networked control theory research,and the problem has been widely concerned by many scholars.But,the research on partial-nodes-based information(PNBI)state estimation for discrete complex networks is not comprehensive enough.Thus,several novel PNBI state estimators are designed for discrete complex networks in this paper based on variance-constraint method.The specific contents are summarized as follows:The state estimation problem is investigated for discrete linear complex networks with stochastic outer coupling strength.The phenomenon of stochastic outer coupling strength is represented by a set of random variable,which obeys the uniform distribution.At the same time,a sequence of Bernoulli random variables is used to describe the sensor delay with certain occurrence probability.Based on the available measurements from partial nodes,a new method of PNBI state estimation is proposed.By using stochastic analysis method,the upper bound matrix of estimation error covariance is obtained,and the optimal estimator parameter is obtained by minimizing the trace of the upper bound matrix.Then,the monotonicity is proved between the occurrence probability of sensor delay and the trace of the upper bound matrix.Finally,a numerical example is given to verify the effectiveness of the proposed PNBI algorithm.The problem of state estimation is discussed for discrete random nonlinearities complex networks with stochastic inner coupling strength.The complex networks have a special kind of nonlinearities and its statistical characteristics are known.The uncertainty of stochastic inner coupling strength is described by multiplicative noise.And the sensor delay with uncertain occurrence probability is characterized by a set of random variables,which obeys Bernoulli distribution.To facilitate reduce the communication burden,a new PNBI state estimator is constructed based on the static event-triggered communication mechanism.The upper bound matrix of the estimation error covariance is given via solving two recursive matrix equations,and an appropriate estimator gain matrix is selected to optimize the trace of the upper bound.Moreover,the monotonicity of the estimator is proved.Finally,a numerical simulation with MATLAB software is carried out to verify the feasibility for the proposed estimator.The PNBI state estimation is proposed for discrete nonlinear complex networks with stochastic inner coupling strength and stochastic outer coupling strength.Firstly,the uncertainty of the stochastic inner coupling strength is denoted by multiplicative noise.The stochastic outer coupling strength is modeled by a set of random variables with uniform distribution.In order to save communication resources further,a PNBI state estimator is designed based on dynamic event-triggered communication mechanism.Secondly,the expression of the upper bound matrix is obtained for the estimation error covariance.The gain matrix of the proposed estimator is calculated by minimizing the trace of the upper bound.Besides,a discriminant condition is given to ensure the uniformly bounded of the trace of the upper bound matrix.Finally,a simulation example is given to verify the correctness of the PNBI estimation method.