Fractional-order complex-variable dynamical network with complex coupling is considered in this paper. The topological structures and system parameters are assumed to be unknown. As we know, the topological structure and system parameters play a key role on the dynamical behavior of complex network. Thus, how to effectively identify them is a critical issue for better studying the network. Through designing proper controllers and updating laws, two corresponding network estimators are constructed. Based on the Lyapunov function method and Gronwall-Bellman integral inequality, the results are analytically derived. Finally, two numerical examples are performed to illustrate the feasibility of the theoretical results.
Topology structure and system parameters have a great influence on the dynamical behavior of dynamical networks. However, they are sometimes unknown or uncertain in advance. How to effectively identify them has been investigated in various network models, from integer-order networks to fractional-order networks with the same order. In the real world, many systems consist of subsystems with different fractional orders. Therefore, the structure identification of a dynamical network with different fractional orders is investigated in this paper. Through designing proper adaptive controllers and parameter updating laws, two network estimators are well constructed. One is for identifying only the unknown topology structure. The other is for identifying both the unknown topology structure and system parameters. Based on the Lyapunov function method and the stability theory of fractional-order dynamical systems, the theoretical results are analytically proved. The effectiveness is verified by three numerical examples as well. In addition, the designed estimators have a good performance in monitoring switching topology. From the practical viewpoint, the designed estimators can be used to monitor the change of current and voltage in the fractional-order circuit systems.
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