Analysis of linear quadratic control loops with decentralized event-triggered sensing: Rate and performance guarantees

We consider a control loop with several distributed sensor agents. Each sensor measures a subset of the states and broadcasts data to a remote controller and the other sensors according to a threshold-based event-triggered policy. This policy specifies that each sensor transmits data when the norm of the error between the actual measurement and an estimate of this measurement exceeds a threshold. The controller incorporates a state estimator relying on the data received from the sensors and enforces a linear feedback control policy. Considering an average quadratic performance index, we provide: (i) upper bounds on the performance of such a decentralized event-triggered policy with respect to the optimal policy when all the agents transmit at maximum rate; and (ii) lower bounds on the average inter-transmission time for the overall networked control system. Moreover, we discuss the conservativeness of the bounds considering some simple cases. The usefulness of the results is highlighted via a numerical example.