Data-Driven Event-Triggered Control Dealing with Noisy Data

This paper is concerned with event-triggered control that deals with noisy data for both discrete-time and continuous-time linear systems with unknown system matrices. First, based on a sufficiently rich finite set of noisy data collected in an experiment, the pair of system matrices is represented as a data-based nominal matrix plus an uncertain matrix with a bounded norm. This formulation enables classical robust control techniques to be applied to tackle the robust control problem. Second, for discrete-time systems, a novel event-triggering condition is proposed, by which an event is triggered if the sum of the squares of the weighted error exceeds the square of the weighted state from the previous event. For continuous-time systems, the event-triggering condition is devised as a monotonically increasing function that starts with a negative value and triggers an event when it reaches zero. This condition can exclude the so-called Zeno behaviour due to its monotonic increase property. Third, by employing a looped functional method, several criteria are derived to co-design suitable state feedback controllers and event-triggering parameters for the systems under study. Finally, the effectiveness of the proposed method is demonstrated through a case study involving a batch reactor system.