Pinning Synchronization for Stochastic Complex Networks with Randomly Occurring Nonlinearities: Tackling Bit Rate Constraints and Allocations

Abstract

In this article, the ultimately bounded synchronization problem is investigated for a class of discrete-time stochastic complex networks under the pinning control strategy. Communication between system nodes and the remote controller is facilitated via wireless networks subject to bit rate constraints. The system model is distinguished by the inclusion of randomly occurring nonlinearities. A coding-decoding transmission mechanism under constrained bit rates is introduced to characterize the digital transmission process. To achieve synchronization of the network nodes with the unforced target node, a pinning controller is specifically devised based on the information from partially selected nodes. Through the application of the stochastic analysis method, a sufficient condition is derived for ensuring the mean-square boundedness of the synchronization error system. In addition, an optimization algorithm is introduced to address bit rate allocation and the design of desired controller gains. Within the presented theoretical framework, the correlation between the mean-square synchronization performance and bit rate allocation is further elucidated. To conclude, a simulation example is provided to substantiate the efficacy of the recommended pinning control approach.