Research On State Estimation Of Complex Networks With Measurement Constraints

Because of its topological structure,universality of application and simplicity of description,complex network is widely used in various fields,such as multi-agent system,neural network and social network.In the past decade,with people's attention to complex network theory and its application,more and more achievements have been made in the study of complex network.However,in real life,sensors in all kinds of systems often cannot measure the internal state value of the system completely,so the research on the system state estimation problem is of great practical significance.In addition,with the increasingly high level of information and intelligence in today's society,how to accurately estimate the state of various complex networks has become a difficult problem explored by many scholars in recent years.In this thesis,the complex network has measurement delay,nonlinear,random coupling and other problems,using appropriate random variables and functions to describe the problem,and according to its characteristics,design the system state estimator,by optimizing the system parameters,to make the designed estimator has better performance.Finally,the performance of the estimator is analyzed by numerical simulation.The specific research contents are as follows:Firstly,the distributed state estimation problem for complex networks with one-step delay is presented.Bernoulli random variables are used to describe the time delay of random variables.Based on unreliable measurements,the state predictor and distributed state estimator for complex networks are designed respectively.The coupling term is eliminated based on Young's inequality and the optimal covariance of state prediction is obtained by combining with the collocation method.At the same time,the state estimation error covariance is obtained by using Young's inequality and design estimator gain,and the iterative formula of state estimation error covariance is obtained based on the prediction error covariance.Using LMI theory,it is proved that the estimator covariance is stable.Finally,a practical multi-agent vehicle system is taken as an example to carry out numerical simulation,and the effectiveness of the estimator and the practicability of the optimized parameters are verified by the comparison of specific data.Secondly,for the problems of random attenuation,nonlinearity and random coupling interference of measured values,attenuation variables are used to describe the attenuation phenomenon of measured values,and Bernoulli random variables are used to describe the random linearity of coupling between nodes.By approximating the nonlinear function with firstorder polynomials and describing the approximating error with lower-order polynomials with bounded coefficients,the integrity of the system state is ensured.Based on the complex network system,the optimal iterative formula of state estimation error is obtained by designing the state estimator and optimizing the gain matrix of the estimator.Finally,through the use of MATLAB software,the process of the whole system is simulated,and the accuracy of the designed distributed state estimator is verified.Finally,on the basis of the research problems in this thesis,the deficiencies of the established system are summarized,and the follow-up research work is planned and prospected.