Structural characterization of optimal event-based controllers for linear stochastic systems

Recent results in networked control systems indicate substantial benefits of event-based control compared to conventional designs. This paper identifies structural properties of optimal event-based controllers designed for stochastic linear systems. The controller is updated by measurements that are sent over a resource-constrained communication channel. The timings for sending updates are determined by an event-trigger whose decisions are based on noisy measurements. The objective is to design event-triggering mechanisms and controllers that optimally meet a trade-off between control performance and average number of update transmissions. It is shown that the optimal controller is a certainty equivalence controller with an affine linear estimator. The optimal event-trigger consists of a Kalman state estimator and a copy of the state predictor at the controller. The difference between both estimates determines, whether to trigger an update transmission. Numerical simulations illustrate the obtained results.