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Event-triggered and self-triggered control design with guaranteed performance

In digital control applications, controllers are typically implemented in a time-triggered fashion, in which control tasks are executed periodically. This design choice is motivated by the fact that it enables the use of a well-developed theory on sampled-data systems. This design choice, however, leads to over-utilization of the available communication resources, and/or a limited lifetime of battery-powered devices, as it might not be necessary to execute the control task every period to guarantee certain closed-loop performance. In fact, this observation leads to the fundamental problem of determining the optimal sampling and communication strategies, where optimality needs to reflect both communication cost as well as control performance. It is expected that the solution to such problems results in control strategies that abandon the time-triggered periodic control paradigm. Two approaches that abandon the periodic communication pattern are event-triggered control (ETC), and self-triggered control (STC). In ETC and STC, the control law consists of two elements: namely, a feedback controller that computes the control input and a triggering mechanism that determines when the control input has to be updated. The difference between event-triggered control and self-triggered control is that in the former the triggering consists of verifying a specific condition continuously and when it becomes true, the control task is triggered, while in the latter at a control update time the next update time is pre-computed. Currently, ETC and STC form popular research areas. However, three important issues have only received marginal attention: (i) the co-design of both the feedback law and the triggering mechanism, (ii) providing performance guarantees by design, and (iii) dealing with constraints on control inputs and states. In this presentation, we propose self-triggered and event-triggered approaches addressing the mentioned issues and allowing to trade guaranteed performance levels with utilization of communication resources. We will consider discrete-time linear systems and the performance will be measured in terms of a standard LQR-type of cost. The methods are such that an LQR cost can be chosen