Distributed Estimation And Optimization Control For The Eigen-spectral Parameters Of Random Opportunistic Networks

Eigen-spectral parameters play an important role in the structure,performance and dynamics of network system.At present,distributed estimation algorithms that can be used for network system characteristic spectrum parameters generally have the following defects: Firstly,it is limited to the network system with fixed structure and is not suitable for the mobile network system.Second,the convergence optimization problem of the estimation algorithm is not thoroughly discussed.The third is usually only the algebraic connectivity and its eigenvector are estimated,which does not involve the estimation of other eigen-spectral parameters.To solve the above problems,this paper designs an estimation algorithm of eigenspectral parameters for random opportunistic network.The key factors affecting the convergence of the estimation algorithm are analyzed and the relationship between them is derived.On this basis,the convergence of the algorithm is optimized.Finally,the estimation algorithm is extended to the estimation and solution of other eigenspectrum.Specific work and contribution include the following three parts:Firstly,the convergence speed of algebraic connectivity estimation algorithm is deduced.The algebraic connectivity estimation algorithm is used to estimate the algebraic connectivity and Fiedler vector of random opportunistic network,and then the convergence condition of the estimation algorithm is analyzed,and the iteration numbers required for the convergence of the estimation algorithm are deduced according to the convergence condition.According to the number of iterations required by the convergence of the algebraic connectivity estimation algorithm and the number of iterations required by the convergence of the averaging algorithm,the iteration number of the averaging algorithm required by the convergence of the algebraic connectivity estimation algorithm is deduced,that is,the convergence speed of the estimation algorithm.Secondly,the convergence rate of stochastic power iteration is optimized.Through the relationship between the number of iterations of average consensus in the stochastic power iteration and the algebraic connectivity of the network,the optimal connectivity of the network algebra is calculated,which makes the convergence of the stochastic power iteration be the fastest.The optimal network connectivity is calculated by the relation between network algebra connectivity and network connectivity.Based on the relationship between network connectivity,network dynamics and communication radius of nodes,the optimal network dynamics and communication radius are calculated under the condition of optimal network connectivity.Secondly,the convergence speed of algebraic connectivity estimation algorithm is optimized.Through the convergence speed formula of the algebraic connectivity estimation algorithm,the optimal algebraic connectivity which makes the convergence speed of the estimation algorithm the fastest is calculated.Through the relation between algebraic connectivity and network connectivity,the optimal network connectivity which makes the convergence speed of the estimation algorithm the fastest is calculated.Based on the relationship between network connectivity and network dynamics and node communication radius,the optimal network dynamics and node communication radius which make the estimation algorithm converge fastest are calculated.Finally,the global characteristic spectrum parameters are generalized.The algebraic connectivity estimation algorithm is extended so that the extended estimation algorithm can estimate the eigenspectrum of the network and the corresponding eigenvectors,and then the Laplace matrix and adjacency matrix of the network are reconstructed by using the estimated eigenvalues and eigenvectors.In conclusion,this paper not only proves the correctness of our algorithm and conclusion theoretically,but also verifies its effectiveness through relevant simulation experiments.