Self - Triggered Control : trading actuation for computation . ∗

Event-triggered and self-triggered control have recently been proposed as alternatives to the well established periodic implementation of control loops on digital platforms. In a self-triggered implementation, the control task is responsible for computing the new actuator values as well as the next instant of time at which the state should be sampled, the control law recomputed, and the actuator values updated. In between these time instants, the system under control requires no attention and can operate in open loop. Self-triggered implementations can be seen as double edged swords: on the one hand, by using the state of the plant to determine when the control law needs to be recomputed, desired levels of control performance are enforced while drastically reducing the resources (processor time, communication bandwidth, etc) used for control; on the other hand, by operating the plant in open loop for extended periods of time, robustness of self-triggered implementations becomes an honest concern. In this paper we propose a self-triggered implementation for linear systems achieving exponential input-to-state stability, hence addressing the robustness concerns. Moreover, the proposed implementation computes the largest possible times during which the plant can operate in open loop while meeting desired performance levels and subject to the computational capabilities of the digital platform. Keyword: Self-triggered control, cyber-physical systems, robustness.