Dynamic Event-Triggered Amplify-and-Forward-Based Model Predictive Control of Polytopic Uncertain Systems

This article investigates the dynamic event-triggered amplify-and-forward (AaF) based model predictive control (MPC) issue of polytopic uncertain systems. As a scheme to enhance the quality of data transmission and extend the transmission distance, an AaF relay is introduced, which is embedded with a new dynamic event-triggered mechanism (DETM) to reduce the relay energy consumption and save the network resources of the relay-to-controller channel. Another DETM of the similar form is embedded into the sensor to conserve the network resources of the senor-to-relay channel. Each of these DETMs contains a time-varying weighting matrix, an additive internal dynamic variable (IDV) and a multiplicative adaptively adjusting variable, which has the advantages of flexibly regulating data sending to decrease the waste of resources while satisfying the performance requirement. A “min-max” MPC problem is proposed, where a robust positively invariant set with the predicted information of the system state and two IDVs is devised. An auxiliary optimization problem constrained by linear matrix inequalities is then presented to obtain the controller parameters. Under the designed MPC algorithm, the auxiliary optimization problem is recursively feasible and the closed-loop system is input-to-state stable. Two examples are provided to validate the proposed dynamic event-triggered AaF-based MPC algorithm and illustrate its superiority.