On LQG-Optimal Event-Based Sampling

Sammanfattning: Event-based control is a promising concept for the design of resource-efficient feedback systems, where events such as sampling, actuation, and data transmissions are triggered reactively based on monitored control performance rather than a periodic timer. In this thesis, we investigate how sampling and communication events should be triggered to fully exploit the potential of event-based control based on the classic linear–quadratic–Gaussian (LQG) framework.The design of the event trigger is formulated as a trade-off between a quadratic cost on control performance and the average event rate. The optimal event trigger is well-known for first-order systems, where it corresponds to a scalar symmetric threshold on the monitored control performance. In this thesis, we consider systems of higher order, where the shape of the optimal threshold is generally unknown. For two new system classes with previously unknown solutions, we prove that the optimal threshold is ellipsoidal for all system orders. Additionally, we propose two numerical methods for finding the optimal threshold shape for general systems.Suboptimal but simpler designs in the form of event-based proportional–integral–derivative (PID) control are also considered. Inspired by results from LQG-optimal sampled-data control, we derive an “ideal” (in the LQG sense) sampled-data PID implementation, from which a range of design options of varying complexity for event-based PID control is proposed. Based on numerical evaluations, we present a proposal implementation that strikes a balance between performance and simplicity. Finally, this thesis also considers stochastic triggering, where events are triggered according to a certain probability. Two policies for stochastic triggering are proposed for a remote state estimation problem, both featuring predictions in the sensor for improved estimation performance. Both policies compare well to other proposals from the literature, and one of the policies also offers significantly simpler performance analysis.