Comparison Perspectives for Time-, Event-, and Self-Triggered Control

Event-based control, subsuming event-and self-triggered control, has the potential to reduce the average triggering rate compared to periodic control while still fulfilling a control objective, e.g., control performance. Different formulations of the inherent performance triggering rate trade-off have been studied to formally show this advantage. One of them compares control performance of triggering schemes under equal average triggering rates. Utilizing this perspective to compare an event-based control scheme to the best periodic control scheme yields the notion of consistency. Alternatively, triggering schemes can be compared with respect to a weighted cost including both control performance and triggering rate. In this work, we discuss the relationship between these different perspectives on comparing triggering schemes, with a particular focus on comparing event-based and periodic control. As a direct outcome, we provide different ways of interpreting consistency (or its absence). Moreover, we discuss key factors in triggering scheme comparisons which can serve as a conceptual basis for the future development of evaluation methods for triggering schemes. With our work, we raise awareness for the importance of triggering scheme evaluations that go beyond numerical examples for one specific parameter choice.