Cluster Synchronization Control for Discrete-Time Complex Dynamical Networks: When Data Transmission Meets Constrained Bit Rate

Observer-Based Bounded H∞ Control for Shift-Varying Linear Repetitive Processes With Constrained Bit Rates Over a Finite Horizon

This technical correspondence examines the issue of observer-based bounded $H_{\infty }$ control for a kind of shift-varying linear repetitive process (LRP) over networks with constrained bit rates in the finite horizon. Unlike the previous researches that address (or avoid) the problem of limited network resources by designing different scheduling protocols, this study focuses on further reducing and optimizing the bandwidth utilization by introducing a bit rate constraint model. Thus, an encoding-decoding mechanism under the constrained bit rates is proposed based on the quantization method. In order to analyze the $H_{\infty }$ performance of the LRP and design an appropriate controller, the LRP is transformed into a shift-varying two-dimensional (2-D) Fornasini-Marchesini model. Sufficient conditions in recursive linear matrix inequalities are proposed to ensure that the extended system achieves a bounded $H_{\infty }$ performance over a finite horizon within the 2-D framework. Furthermore, a component-based strategy for allocating the bit rates is provided to expand the quantization region under the constraint of bit rates. Finally, the effectiveness of the proposed method is verified by a simulation example.

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

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.