Uniformly Ultimate Boundedness Control with Decentralized Event-Triggering

Abstract

Event-triggered control is a method that the control input is updated only when a certain condition is satisfied (i.e., an event occurs). In this paper, event-triggered control over a sensor network is studied based on the notion of uniformly ultimate boundedness. Since sensors are located in a distributed way, we consider multiple event-triggering conditions. In uniformly ultimate boundedness, it is guaranteed that if the state reaches a certain set containing the origin, the state stays within this set. Using this notion, the occurrence of events in the neighborhood of the origin is inhibited. First, the simultaneous design problem of a controller and eventtriggering conditions is formulated. Next, this problem is reduced to an LMI (linear matrix inequality) optimization problem. Finally, the proposed method is demonstrated by a numerical example.

LMI-Based Design of Output Feedback Controllers with Decentralized Event-Triggering

“…Next, since we consider the asymptotic stability, communications always occur in the steady state. To avoid such communications, it is important to use the notion of uniformly ultimate boundedness [1], [10], [17], [21]. Third, in this paper, the parameter σ i in the event-triggering condition (4) is given in advance.…”

“…In the above problem, we consider finding a controller under the assumption where the threshold of an event-triggering condition is given. Such approaches have also been studied in e.g., [8], [10], [15], [16], [20]- [23]. Since in event-triggered control, there are uncertainties in the measured value managed in a controller, it may be appropriate to design a controller considering these uncertainties together with model uncertainties and disturbances.…”

Output Feedback Ultimate Boundedness Control with Decentralized Event-Triggering

“…In design of event-triggered state-feedback controllers based on uniformly ultimate boundedness, some results using an LMI (linear matrix inequality) technique have been obtained in [16], [18], [19]. An LMI feasibility/optimization problem is a convex programming problem that can be efficiently solved.…”