事件触发非周期间歇控制下离散时滞系统的指数镇定
Exponential Stabilization of Discrete-time Delayed Systems under Event-triggered Aperiodic Intermittent Control
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摘要: 本文研究事件触发非周期间歇控制下离散时滞系统的指数镇定问题。针对离散时滞系统,分别设计了基于事件触发的非周期间歇控制(EAPIC)方案和基于状态控制宽度的事件触发非周期间歇控制(EAPIC-SCW)方案。在EAPIC方案下,应用阈值和检测周期指标,给出了EAPIC的算法,导出了指数稳定性判据。并通过在EAPIC中引入自由控制指标,设计了EAPIC-SCW方案。理论上证明了设计的EAPIC和EAPIC-SCW是非平凡的,且能让离散时滞系统获得所需的指数稳定性。而且,为了体现事件触发非周期间歇控制的性能,对包括周期间歇控制、时间触发非周期间歇控制在内的控制方案的控制次数和极小控制率进行了理论比较,理论结果表明两种事件触发非周期间歇控制的控制次数和极小控制率更低。最后,用数值仿真例子验证了理论结果的有效性。结果表明EAPIC和EAPIC-SCW在100 s内的控制次数和控制率分别为10次、56%和12次、38%,拥有比周期间歇控制和时间触发非周期间歇控制更低的控制次数和控制率,并且EAPIC-SCW具有最低的控制率和最短的总控制时长。Abstract: This paper studies the exponential stabilization of discrete-time delayed systems under event-triggered aperiodic intermittent controls. For discrete-time delayed systems (DDSs), an event-triggered aperiodic intermittent control (EAPIC) scheme and an EAPIC based on state control width (EAPIC-SCW) scheme are designed, respectively. Under the EAPIC scheme, by applying thresh-old and detection period index, an algorithm for event-triggered aperiodic intermittent control is given, and the exponential stability criterion is derived. In addition, an EAPIC-SCW scheme is designed by introducing free control indicators into EAPIC. It is theoretically proved that the designed EAPIC and EAPIC-SCW are non-trivial and can achieve the required exponential stability of the discrete-time delayed system. To assess the performance of these schemes, control times and minimal rate of control are compared between the periodic intermittent control scheme and the time-triggered aperiodic intermittent control scheme. Our theoretical results show that both event-triggered controls offer lower control times and rates. Theoretical results show that both the control times and minimum control rates of the two kinds of event-triggered aperiodic intermittent control are lower. Finally, a numerical simulation example is used to verify the effectiveness of the theoretical results. The results show that the control times and control rates of EAPIC and EAPIC-SCW in 100 seconds are 10 times, 56% and 12 times, 38%, respectively, which are lower than that of the periodic intermittent control and the time-triggered aperiodic intermittent control, and EAPIC-SCW achieves the lowest control rate and the shortest total control time.