Chapter 17 - Event-triggered and self-triggered control for networked feedback systems with delay and packet dropout

Abstract

Time delays and packet dropouts are two conspicuous phenomena in networked feedback control systems, and constitute hindrance to system performance. Often in such systems the delays can be long and time varying, and in the extreme due to network congestion, result in packet dropouts, even leading to system instability. A challenging problem in the design of networked control systems (NCSs) is, therefore, to cope with the negative impact of time delays and packet dropouts. This chapter investigates the stabilization of such networked feedback systems with time-varying network-induced delays and packet dropouts under limited communication resources. We use a switched system model to describe the time-varying characteristics of network-induced delays, which are characterized by the bound and variation rate of the delay. Compatibly to this model description, we employ switched systems synthesis techniques to design a stabilizing switching controller, whose distinctive advantage enables us to bypass the difficult construction of complex Lyapunov-Krasovskii functionals that are otherwise necessary. The approach leads to several results, partly solvable by solving some linear matrix inequalities, for which efficient numerical algorithms are available, and partly by iterative procedures via switching sequences. First, the existing condition on an exponentially stabilizing event-triggered state feedback switching controller is proposed to stabilize the NCS in the presence of short network-induced delays. Second, with an appropriately designed event-triggered switching controller, the NCS is shown to be exponentially stabilized in the joint presence of short network-induced delays and packet dropouts. Finally, self-triggered conditions are obtained to ensure that the control law remains effective. Conceptually, it is useful to note that the proposed event-triggered threshold depends on the maximum allowable number of successive packet dropouts, while the self-triggered time interval is monotonically increasing with the average dwell time, implying that with a slower rate in delay variation, the longer is the trigger interval.