Periodic event-triggered networked control systems subject to large transmission delays

This paper studies periodic event-triggered networked control for nonlinear systems, where the plants and controllers are connected by multiple independent communication channels. Several network-induced imperfections are considered simultaneously, including time-varying inter-sampling times, sensor node scheduling, and especially, large time-varying transmission delays, where the transmitted signal may arrive at the destination node after the next transmission occurs. A new hybrid system approach is provided to model the closed-loop system that contains all communication related behavior. Then, by constructing new storage functions on the system state and updating errors, the relationship between the maximum allowable sampling period (MASP) and maximum allowable delay number in sampling (MADNS) is analyzed, where the latter denotes how many inter-sampling periods can be included in one transmission delay. Moreover, to efficiently reduce unnecessary transmissions, a new dynamic event-triggered control scheme is proposed, where the event-triggering conditions are detected only at aperiodic and asynchronous sampling instants. From emulation-based method, where the controllers are initially designed by ignoring all the network-induced imperfections, sufficient conditions on the dynamic event-triggered control are given to ensure closed-loop input-to-state stability with respect to external disturbances. Moreover, according to different capacities of the communication channels, the corresponding implementation strategies of the designed dynamic event-triggered control schemes are discussed. Finally, two nonlinear examples are simulated to illustrate the feasibility and efficiency of the theoretical results.