Output-Based Dynamic Periodic Event-Triggered Control with Application to the Tunnel Diode System

Abstract

The integration of communication channels with the feedback loop in a networked control system (NCS) is attractive for many applications. A major challenge in the NCS is to reduce transmissions over the network between the sensors, the controller, and the actuators to avoid network congestion. An efficient approach to achieving this goal is the event-triggered implementation where the control actions are only updated when necessary from stability/performance perspectives. In particular, periodic event-triggered control (PETC) has garnered recent attention because of its practical implementation advantages. This paper focuses on the design of stabilizing PETC for linear time-invariant systems. It is assumed that the plant state is partially known; the feedback signal is sent to the controller at discrete-time instants via a digital channel; and an event-triggered controller is synthesized, solely based on the available plant measurement. The constructed event-triggering law is novel and only verified at periodic time instants; it is more adapted to practical implementations. The proposed approach ensures a global asymptotic stability property for the closed-loop system under mild conditions. The overall model is developed as a hybrid dynamical system to truly describe the mixed continuous-time and discrete-time dynamics. The stability is studied using appropriate Lyapunov functions. The efficiency of the technique is illustrated in the dynamic model of the tunnel diode system.

Keywords

• periodic event-triggered control
• tunnel diode
• linear systems
• hybrid dynamical systems