text: AbstractWe consider a stochastic system where the communication between the controller and the actuatoris triggered by a threshold-based rule. The communication is performed across an unreliable link thatstochastically erases transmitted packets. To decrease the communication burden, and as a partial pro-tection against dropped packets, the controller sends a sequence of control commands to the actuator ineach packet. These commands are stored in a buffer and applied sequentially until the next control packetarrives. In this context, we study dead-beat control laws and compute the expected linear-quadratic loss ofthe closed-loop system for any given event-threshold. Furthermore, we provide analytical expressions thatquantify the trade-off between the communication cost and the control performance of event-triggeredcontrol systems. Numerical examples demonstrate the effectiveness of the proposed framework.Index TermsEvent-triggering algorithms; Linear systems; Communication networks; Packet loss; Networkedcontrol
  @cite_36: For a single control loop with communication rate constraints, Event-triggered control often outperforms periodic control. When multiple loops are being controlled over a shared contention-based medium, however, the advantage of event-triggered policies is less well understood. In this paper, we consider event-triggered impulse control under lossy communication. The sampling events are determined by level crossings of the plant output. It is shown how a stochastic control criterion depends on the level thresholds and the packet loss probability for a class of integrator plants. For multiple control loops, this result is used to derive a design guideline on how to assign the levels that lead to optimal use of the available communication resources. It is shown that the structure of the event generator depends critically on the loss probability.
  @cite_27: The normal approach to digital control is to sample periodically in time. Using an analog of integration theory we can call this Riemann sampling. Lebesgue sampling or event based sampling is an alternative to Riemann sampling. It means that signals are sampled only when measurements pass certain limits. In this paper it is shown that Lebesgue sampling gives better performance for some simple systems.
  @cite_4: In this work, we analyze event-based control for scalar systems with an impulsive input that resets the state to the origin when applied. The event information is transmitted within packets, which are randomly dropped. We derive the cost as well as the expected times between events and discuss how to change the bounds, which generate the events, after a packet loss.
  @cite_6: We investigate control of a non-linear process when communication and processing capabilities are limited. The sensor communicates with the controller node through an erasure channel which introduces independent and identically distributed (i.i.d.) packet dropouts. Processor availability for control is random and, at times, insufficient to calculate plant inputs. To make efficient use of communication and processing resources, the sensor transmits only when the plant state lies outside a bounded target set. Control calculations are triggered by the received data. If a plant state measurement is successfully received and while the processor is available for control, the algorithm recursively calculates a sequence of tentative plant inputs, which are stored in a buffer for potential future use. This safeguards for time-steps when the processor is unavailable for control. We derive sufficient conditions on system parameters for stochastic stability of the closed loop and illustrate performance gains through numerical studies.
summary: The analysis becomes even more involved when the network is unreliable. Blind and Allg " o wer @cite_4 extended the work of @cite_27 to the case where transmissions from the sensor to the controller take place over an unreliable link. They analytically derived the control cost and the expected inter-event times for different packet loss rates. Rabi and Johansson @cite_36 designed the optimal impulse control and the level triggering mechanism under packet losses with multiple loops sharing a common network. From a different perspective, @cite_6 analyzed the stability of an event-triggered implementation of a controller in the presence of packet losses and limited processing resources. However, in all these works, the unreliable channel appears between sensor and controller, while the controller-actuator communication is lossless.