On Minimum-Variance Event-Triggered Control

We study the problem of minimum-variance event-triggered output-feedback control of linear time-invariant processes driven by white Gaussian noise. We show that the optimal event generation is separated from the controller configuration and can be determined by solving an optimal stopping problem. Then, for the case of integrator processes, we extend the Lebesgue sampling result of Åström and Bernhardsson in two directions: 1) we show that it applies to systems with measurement noise and limited control effort and 2) we prove that in the scalar case this control strategy is optimal, in a sense that no other causal event-triggered sampled-data controller with the same average sampling rate can outperform it.