Finite‐time optimal pinning control and synchronization for partially interdependent networks

Abstract

Summary For partially interdependent networks composed of two subnetworks, the finite‐time optimal pinning control problem is investigated. Among them, only a part of the nodes between the two subnetworks are interdependent on each other. In the network, the coupling relationship between any two nodes of the network is a continuous nonlinear function. Based on the pinning control, the optimal control theory, Kalman's controllability rank conditions, and introducing the Lagrange function and applying controllers to the partial nodes of the network, we propose some characterization indicators which ensure that the two subnetworks of partially interdependent networks can synchronize to the equilibrium points of their isolate systems, separately. Finally, some numerical simulations are performed on the partially interdependent networks including two small world subnetworks. The results show that the optimal pinning control method proposed in this article can greatly reduce the control costs and achieve the ideal synchronous status quickly.

Event‐triggered finite‐time quantized synchronization of uncertain delayed neural networks

“…In Reference 32, an observer‐based adaptive FT tracking control strategy was proposed, and the stability for presented system was formulated based on semi‐global practical FT stability theory. The FT optimal pinning control problem for partially interdependent networks composed of two subnetworks was studied in Reference 33 by introducing the Lagrange function. However, no results about the FT synchronization problem were investigated for uncertain delayed NNs based on a unified architecture that integrates ET mechanisms, and quantization, which motivates the present work.…”

“…Motivated by above discussion, we summed up the contribution of our work in the following points. (i) The FT synchronization problem of uncertain time‐delay NNs with input quantization is first proposed; (ii) A new ET scheme coordinated with quantized and ET mechanism is applied to release the excessive occupancy of limited network bandwidth, compared with ET scheme used in References 24 and 33, the ET scheme developed in this article has a better performance of reducing some unnecessary transmissions of system dynamics; (iii) By constructing a Lyapunov functional, a sufficient condition for uncertain time‐delay NNs is obtained by using the matrix inequality of free‐weighting matrix techniques and some lemmas, which guarantees the FT synchronization for error system. And when considering the FT synchronization problem for error system, in order to overcome the difficulty that some inequalities are not LMIs, the sufficient condition for the existence of a state feedback controller expressed by LMI is proposed by using the method of separating variables, which is different from other controller rules directly obtained 34 …”