Data-driven Event-triggered Control for Discrete-time LTI Systems

Inspired by recent work on data-driven control, this work presents data-driven event-triggered control strategies for discrete-time linear time-invariant (LTI) systems. The results presented do not require explicit identification of the system parameters and are based on the input and state data collected from the system during an open-loop experiment. The design of event-triggered control consists of two stages: finding a state feedback controller that exponentially stabilizes the system and designing an event-triggered policy that determines the instances at which the control law needs to be updated. The proposed designs in both stages involve solving semi-definite programs with data-dependent linear matrix inequalities (LMIs) as constraints. For the event-triggered implementation, we employ a relative thresholding mechanism and the range of the thresholding parameter is derived using S-procedure. Conditions on the thresholding parameter are derived that ensure both pre-specified exponential convergence and non-trivial event-triggering. We present simulation results for an illustrative example that validates the proposed methods.