Self-triggered and event-driven control for linear systems with stochastic delays

Delays are often present in embedded and networked control loops and represent one of the main sources of performance limitations. In this paper, we propose two aperiodic control strategies to optimize closed-loop performance in the presence of stochastic delays: (i) a self-triggered strategy, in which the deadline to drop data is decided on-line based on the current state; (ii) an event-driven strategy, whereby the control input is updated immediately after the delayed data becomes available, leading in general to faster but time-varying control loops. These schemes are designed and analyzed using a standard LQG framework, which allows for assessing and comparing closed-loop performance. We establish that our self-triggered strategy always achieves a better closed-loop performance than periodic control with an optimal sampling period. Moreover, we provide examples where the event-driven strategy outperforms the self-triggered strategy and examples where the opposite is observed.