Event-Triggered Data-Driven Predictive Control for Multirate Systems: Theoretic Analysis and Experimental Results

This article presents an event-triggered data-driven predictive control approach for unknown linear time-invariant (LTI) multirate systems subject to bounded measurement noise. First, an implicit model description for a multirate unknown LTI system is introduced, which uses the map of a Hankel matrix to characterize trajectories of the system. Then, a data-driven compact lifting technique is designed, leading to a lower order lifted fast sampled output signal with norm preserved property compared with the fully lifted signal. An event-triggering mechanism is designed based on the accumulation of the error between the multirate measurement and predicted output. This is designed to trigger the execution of optimization for data-driven predictive control, resulting in the decrease of computation resource. Moreover, the recursive feasibility and the uniformly ultimately bounded stability of the control system is analyzed. Finally, the effectiveness of the proposed approach is illustrated through the application to a robot arm. Compared with a single rate data-driven predictive control approach and a feedforward PID control approach, the proposed approach achieves 2% and 3% improvement in terms of the tracking accuracy, and the number of optimization performed is reduced by 27%.