Periodic event-triggered control of nonlinear systems using overapproximation techniques

• Published in: Automatica (Oxford) Vol. 94; pp. 81 - 87
• Main Authors: Borgers, D.P., Postoyan, R., Anta, A., Tabuada, P., Nešić, D., Heemels, W.P.M.H.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.08.2018; Elsevier
• Subjects: Automatic; Continuous time systems; Digital implementation; Engineering Sciences; Event-triggered control; Nonlinear systems; Polytopic overapproximation; Sampling periods; Continuous time systems; Polytopic overapproximation; Event-triggered control; Nonlinear systems; Sampling periods; Digital implementation
• ISSN: 0005-1098; 1873-2836; 1873-2836
• DOI: 10.1016/j.automatica.2018.04.019

In event-triggered control, the control task consisting of sampling the plant’s output and updating the control input is executed whenever a certain event function exceeds a given threshold. The event function typically needs to be monitored continuously, which is difficult to realize in digital implementations. This has led to the development of periodic event-triggered control (PETC), in which the event function is only evaluated periodically. In this paper, we consider general nonlinear continuous event-triggered control (CETC) systems, and present a method to transform the CETC system into a PETC system. In particular, we provide an explicit sampling period at which the event function is evaluated and we present a constructive procedure to redesign the triggering condition. The latter is obtained by upper-bounding the evolution of the event function of the CETC system between two successive sampling instants by a linear time-invariant system and then by using convex overapproximation techniques. Using this approach, we are able to preserve the control performance guarantees (e.g., asymptotic stability with a certain decay rate) of the original CETC system.