Time-triggering versus event-triggering control over communication channels

Time-triggered and event-triggered control strategies for stabilization of an unstable plant over a rate-limited communication channel subject to unknown, bounded delay are studied and compared. Event triggering carries implicit information, revealing the state of the plant. However, the delay in the communication channel causes information loss, as it makes the state information out of date. There is a critical delay value, when the loss of information due to the communication delay perfectly compensates the implicit information carried by the triggering events. This occurs when the maximum delay equals the inverse of the entropy rate of the plant.<div><br></div><div><p>When the delay is small, the timing information carried by the triggering events is substantial and ensures that controller can stabilize the system. In contrast, for small values of the delay the information transmission rate required by a time-triggered implementation equals the rate required by the classic data-rate theorem.</p> <p>For large delay values the event-triggered design converge to an asymptote the time-triggered result grows linearly as γ→∞. The reason for this difference is that, the time-triggered design depends only on delay while the event-triggered scheme depends on both state and delay.</p></div>