Dynamics Analysis And Parameter Identification Of Networked Stochastic Hybrid Systems

As an important issue in the community of network science,the dynamic synchronization of complex networks is usually adopted to interpret the collective and coordinated behaviors of complex systems in nature and human society.Since the network topology and parameters play critical roles in the evolution of the dynamical behavior of the complex system,the corresponding identification problem of unknown dynamic parameters and topological structure are of strong scientific significance practical values in reality.Specifically,the problems of parameter identification are more challengeable when the complex system is disturbed by a variety of random noises.This paper mainly concentrates on the synchronization of randomly coupled harmonic oscillators,the parameter and topology identification of stochastic complex networks,and the changeable topology identification of a stochastic second-order multi-agent networks with Markovian jumping.The main contributions are summarized as follows:1.Firstly,we investigate the synchronization dynamics of coupled harmonic oscillators with stochastic disturbed inputs.A more generic distributed input control is designed only based on the stochastic disturbed relative position states among the harmonic oscillators.The synchronized dynamical behaviors of the stochastic coupled harmonic oscillators are analyzed in virtue of the algebraic graph theory,the matrix analysis theory,the stability theory of stochastic differential equation and the It? formula with the proposed protocol.Some sufficient criteria on almost surely synchronization of the coupled harmonic oscillators are obtained theoretically.2.Secondly,we discuss the issues of dynamic parameters and topology identification of complex networks with stochastic disturbances.A new approach is proposed to simultaneously identify the dynamic parameters and topologies of a complex networks with random perturbations based on an effective adaptive control law.The results show that dynamic parameters and topologies can be effectively identified since the error dynamic network always achieve almost sure stability with and without both communication delays and coupling delays.The method is also applicable to the stochastic complex networks with coupling delays and nodes delays.3.Finally,the identification of changeable topologies of a stochastic second-order multi-agent networks with Markovian jumping is studied under an effective adaptive law.It is proved that the new error dynamical networks are both almost surely stable with and without time delays.By the ergodicity and memoryless of a continuous time finite homogeneous irreducible Markov chains,a novel parameter identification strategy is proposed to identify the specific topology via a set of sequences which approaches the topology structure.The changeable topologies of a stochastic second-order multi-agent networks are successfully identified in the process of "external synchronization" between the driving network and response network.The numerical simulations further verify the correctness of the theoretical results and the validity of the adaptive law.