Topology identification for stochastic multi-layer networks via graph-theoretic method

The topological structures of multi-layer networks have an important influence on their dynamical properties, but in most cases the topological structures of networks are unknown. Hence, this paper pays attention to investigating topology identification problems for multi-layer networks with stochastic perturbations. Both intra-layer coupling and inter-layer coupling are incorporated into the research model. Based on the graph-theoretic method and Lyapunov function, topology identification criteria for stochastic multi-layer networks are obtained by designing a suitable adaptive controller. Furthermore, to estimate the time of identification, the finite-time identification criteria are obtained by finite-time control technique. Finally, double-layer Watts-Strogatz small-world networks are presented for numerical simulations to illustrate the correctness of theoretical results.