Event-Triggered Control

Abstract

AbstractThis chapter investigates versions of the event-triggered control problem for discrete-time switched linear systems with network transmission delays. In the first version, it is assumed that the controller can only access the transmitted information of system state and mode at each event-triggered instant. A mode-dependent event-triggered transmission scheme is proposed and the closed-loop system is modeled as a switched system with delayed state and augmented switching signal. Then based on the multiple Lyapunov functional method, an exponential stability condition and design method for state feedback controller gains are obtained. The proposed approach leads an important step to study the event-triggered control for discrete-time switched systems. Finally, the effectiveness and improvement of the proposed approach are illustrated by a numerical example. In the second version, we examine the design of event-triggered static and dynamic feedback controllers for discrete-time linear systems. For the efficiency of energy, we make the first attempt to devise a switching event-triggered mechanism (ETM) which is characterized by a switching between the discrete-time sampled-data control and the common continuous ETM. In this sense, the event detector has a waiting time interval after sending a sampling signal. This method facilitates to enlarge the lower bound of inter-execution intervals so that the number of samplings can be reduced essentially. The issue of actuator saturation is also considered in this chapter. By generalized sector condition, a switching Lyapunov functional is constructed to derive the sufficient conditions such that the discrete-time linear systems are local stable. Based on the stability conditions, the calculation methods are provided to solve both the desired control gains and the triggering parameters. Finally, numerical simulations are given to validate the effectiveness and superiority of the proposed method. In the third part, we direct attention to the analysis and design of adaptive event-triggering scheme (AETS) for both discrete-time nonlinear and linear systems. What makes AETS different from static event-triggering scheme (SETS) is that an auxiliary dynamic variable satisfying a certain difference equation is incorporated into the event-triggering condition. The sufficient conditions of asymptotic stability of the closed-loop event-triggered control systems under both two triggering schemes are given. Especially, for the linear systems case, the minimum time between two consecutive control updates is discussed. Also, the quantitative relation among the system parameters, the preselected triggering parameters in AETS, and a quadratic performance index are established. Finally, the effectiveness and respective advantage of the proposed event-triggering schemes are illustrated on a practical example.KeywordsDiscrete-time switched systemEvent-triggered controlAverage dwell timeExponential stabilitySwitching event-triggered mechanismSwitching Lyapunov functionalAdaptive event-triggering schemeStatic event-triggering schemeDiscrete-time nonlinear systemsAuxiliary variable