Model-Based Periodic Event-Triggered Control Strategy to Stabilize a Scalar Nonlinear System

This article focuses on the problem of stabilizing a scalar continuous-time nonlinear system under bounded network delay and process noise. In order to save the feedback network's bandwidth, a model-based periodic event-triggered control policy is utilized to maintain longer intersampling intervals, which are at least as long as the sampling period of periodic policies. Furthermore, the event-triggering condition is only checked intermittently at fixed time instants, i.e., the sampling time instants. Without acknowledgment (ACK), the updating of nominal models at the sensor and at the controller are asynchronous. The two cases, where the network delay is either less than the sampling period or larger than the sampling period, are investigated. In comparison with periodic sampling methods, our scheme can make full use of the received data packets, particularly their sampling time instant information, which yields a lower occupied bit rate while guaranteeing the desired input-to-state stability. Note that the obtained bit rate conditions are only related to the Lipschitz parameter, the bound of network delay, the number of quantization bits, and the sampling period. The bounded process noise will not incur any increase of the stabilizing bit rate under the proposed strategy.