Control systems are becoming more efficient, more sustainable and less costly by the convergence with networking and information technology. The limited digital channel capacity, however, can degrade or even destroy control systems. To maintain system performance with the limited digital channel capacity, event triggered transmission, with which transmission is triggered by a certain event, is proposed. Our research is to analytically examine the tradeoff between system performance and digital channel capacity in event triggered systems.;We first study the optimal communication rule which minimizes mean square state estimation error with limited channel capacity. By introducing a cost for each transmission, the optimal communication rule which minimizes the average mean square state estimation error discounted by the transmission cost is shown to be event triggered. Because the optimal event trigger is difficult to compute, computationally efficient suboptimal event trigger is presented. Our simulation results show that we can compute tighter upper bounds on the suboptimal costs and tighter lower bounds on the optimal costs than the prior works in [13, 11, 34], while guaranteeing comparable actual costs. Based on the same idea, computationally efficient weakly coupled suboptimal event triggers for both sensor and controller are also designed for output feedback control systems to minimize the mean square state with limited channel capacity. By weakly coupled, we mean that the transmission from sensor to controller doesn't not necessarily trigger the transmission from controller to actuator, and vice versa. The weakly coupled transmissions represent an advance over the synchronized transmissions proposed in [15], especially in multi-sensor systems.;The work above, however, ignores the influence of network delay and quantization error. We, then, consider both the network delay and quantization error in event triggered control systems to guarantee input-to-state stability (ISS) and resilience, respectively. We first give a sufficient condition to guarantee both ISS and efficient attentiveness in event triggered control systems. An event triggered system is efficiently attentive if longer inter-sampling interval and lower instantaneous bit-rate, the ratio between the number of bits in a packet to the acceptable delay of this packet, can be achieved when the system state apporaches the origin. Most well designed event triggered systems are efficiently attentive, but a counter example was given in [37] to show that not all event triggered systems are efficiently attentive. To our best knowledge, our work in [37] is the first one which studies efficient attentiveness of event triggered systems. Efficiently attentive event triggered systems usually have long inter-sampling interval, which raises a concern about whether event triggered systems are resilient to unexpected disturbances. To address this concern, we, then, study the resilience of event triggered control systems to transient unknown magnitude disturbances. To our best knowledge, this is the first time the resilience of event triggered systems is studied. We run the event triggered system under two different regimes: safe an d unsafe, according to whether the system is hit by a transient unknown magnitude disturbance. If the system is under safe regime, both sufficient instantaneous bit-rate and necessary instantaneous bit-rate for asymptotic stability are provided. If the system is under unsafe regime, a sufficient instantaneous bit-rate is given to guarantee resilience, i.e. the system can come back to a neighborhood of the origin in a finite time.
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