Novel criteria of sampled-data synchronization controller design for gated recurrent unit neural networks under mismatched parameters

Synchronization between neural networks (NNs) has been intensively investigated to analyze stability, convergence properties, neuronal behaviors and response to various inputs. However, synchronization techniques of NNs with gated recurrent units (GRUs) have not been provided until now due to their complicated nonlinearity. In this paper, we address the sampled-data synchronization problems of GRUs for the first time, and propose controller design methods using discretely sampled control inputs to synchronize master and slave GRUs. The master and slave GRUs are mathematically modeled as a linear parameter varying (LPV) system in which the parameter of the slave GRUs is constructed independently of the master GRUs. This distinctive modeling feature provides flexibility to extend the existing master and slave NNs into a more general structure. Indeed, the sampled-data synchronization can be achieved by formulating the design condition in terms of linear matrix inequalities (LMIs). The novel sampled-data synchronization criteria are devised by combining the H _∞ controller design with the looped-functional approach. The synthesized synchronization controllers guarantee not only asymptotic stability of the synchronization error system with aperiodic sampling, but also provides a satisfactory H _∞ control performance. Moreover, the communication efficiency is improved by using the proposed method in which the sampled-data synchronization controller is combined with the event-triggered mechanism. Finally, the numerical example validates the proposed theoretical contributions via simulation results.