Asynchronously Delayed Intermittent Control for Highly Nonlinear Stochastic Delayed Large-Scale Networks

This paper investigates the stabilization of highly nonlinear stochastic delayed large-scale networks (HSDLN) based on asynchronously delayed intermittent decentralized control (ADIDC). By incorporating highly nonlinearity into the networks, practical problems can be more accurately modeled, and the nonlinear coupling relationships among nodes can be effectively captured, vastly expanding the practical application scope. ADIDC effectively integrates the advantages of asynchronously intermittent decentralized control and delayed intermittent control, enabling the networks to achieve the desired behavior. Subsequently, we set up an auxiliary timer and then define a newfangled Lyapunov functional. In particular, an innovative Lyapunov-based analysis, not utilizing Halanay-type differential inequality, is introduced to obtain a stabilization criterion for HSDLN, which effectively copes with asynchronously intermittent decentralized control and highly nonlinear, stochastic, and delayed elements. Meanwhile, a graph-theoretic methodology is employed to address the cross-terms arising in an asynchronous sense. Ultimately, as a practical application of the theoretical findings, a class of FitzHugh-Nagumo models is considered, and the stabilization is validated through numerical simulations.
Note to Practitioners
—This paper is motivated by existing results on various intermittent controls for the dynamics of complex networks. The existing results mainly require intermittent controls to be continuously/discretely synchronous sampled-data each node of complex networks, which limits the application scope of intermittent controls. This paper designs a new hybrid control called asynchronously delayed intermittent decentralized control. Particularly, asynchronously intermittent sampled-data control is a special case of control in this paper. Moreover, some lower conservative sufficient conditions are derived, such as local Lipschitz condition and polynomial growth condition instead of global Lipschitz condition and linear growth condition for coefficients of complex networks, and the average work time ratio instead of the maximum rest time ratio for intermittent control. The proposed results provide a novel idea for the stabilization study of FitzHugh-Nagumo models, and it is expected that the proposed methods can be extended to more actual physical engineering systems.