Discrete-Time Event-Triggered Control of Nonlinear Wireless Networked Control Systems

Hindawi Publishing Corporation Abstract and Applied Analysis Volume 2014, Article ID 860438, 14 pages http://dx.doi.org/10.1155/2014/860438 Research Article Discrete-Time Event-Triggered Control of Nonlinear Wireless Networked Control Systems Songlin Hu,1,2 Dong Yue,2 Min Shi,2 and Xiangpeng Xie2 1 2 College of Automation, Nanjing University of Posts and Telecommunications, Nanjing 210023, China Institute of Advanced Technology, Nanjing University of Posts and Telecommunications, Nanjing 210023, China Correspondence should be addressed to Dong Yue; Received 10 April 2014; Accepted 4 May 2014; Published 20 May 2014 Academic Editor: Bo Shen Copyright © 2014 Songlin Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This paper investigates the problem of stabilization of nonlinear discrete-time networked control systems (NCSs) with eventtriggering communication scheme in the presence of signal transmission delay. A Takagi-Sugeno (T-S) fuzzy model and paralleldistributed compensation (PDC) scheme are first employed to design a nonlinear fuzzy event-triggered controller for the stabilization of nonlinear discrete-time NCSs. The idea of the event-triggering communication scheme (i.e., a soft computation algorithm) under consideration is that the current sensor data is transmitted only when the current sensor data and the previously transmitted one satisfy a certain state-dependent trigger condition. By taking the signal transmission delay into consideration and using delay system approach, a T-S fuzzy delay system model is established to describe the nonlinear discrete-time NCSs with eventtriggering communication scheme. Attention is focused on the design of fuzzy event-triggered controller which ensures asymptotic stability of the closed-loop fuzzy systems. Linear matrix inequality- (LMI-) based conditions are formulated for the existence of admissible fuzzy event-triggered controller. If these conditions are feasible, a desired fuzzy event-triggered controller can be readily constructed. A nonlinear mass-spring-damper mechanical system is presented to demonstrate the effectiveness of the proposed method. 1. Introduction Recently, networked control systems (NCSs) have been drawing more and more attention from researchers working in the areas of system and control due to their low cost, high flexibility, and simple installation and maintenance [1], and a lot of important works have been reported; see, for example, [2–16]. These works have significant importance on both theoretical advancement and practical applications of NCSs. However, it should be pointed out that the time-triggered (or periodic-triggered) transmission scheme is adopted in the aforementioned works. Using the time-triggered transmission scheme implies that all the sampled data need to be transmitted through communication networks regardless of the state of the controlled plant. As is well known, the sampling period is determined according to the worst case operation conditions that rarely occur, and thus the periodic transmission scheme may result in conservative usage of the limited communication bandwidth in the context of NCSs. On the other hand, with the development of network communication technology, the network bandwidth is significantly improved such as Ethernet (100 MB/s) and WiFi (11 MB/s), while there are also some types of network with low bandwidth for the purpose of control or power saving such as CAN (1 MB/s) and Zigbee (250 Kb/s). In these networks, if the number of sensors is large, network traffic may be very high. In this case, the reduction of data transmission rate is necessary and most feasible. Therefore, it is significant to investigate how to improve the bandwidth utilization in data transmission so that network bandwidth can be used for other traffic. To save the limited bandwidth, one can make use of the so-called sporadic transmission scheme. As indicated in [17], event-based/triggered transmission scheme (EBTS/ETTS) just represents one way of generating such sporadic transmissions. EBTS has many potential advantages for NCSs, such as clock-free operation, less traffic requirement, and better resource utilization. Specifically, under the EBTS, the 2 sampled signals need to be transmitted only when some internal measure of the novelty in the sampled information exceeds a specified threshold, which implies that only part of the sampled signals is transmitted from the sensor to the controller, and the redundant signals are filtered in the sensor node. This, in turn, will generate a sporadic sequence of controller invocations. It is expected that the average rate of event-triggered task set will be much lower than the rate of a comparable time-triggered task set [17]. Hence, EBTS can be viewed as the possible and important alternative to time-triggered transmission scheme in terms of the network bandwidth utilization. In the last five years, the research on EBTS has received considerable attention, and many interesting EBTSs have been developed in the literature to reduce the network bandwidth utilization; see, for example, [18–27] and the references therein. However, it is worth mentioning that the event-triggering conditions proposed in aforementioned publications need to be checked at every sampling instant, which leads to the higher computation cost of the smart sensor. Very recently, Peng and Yang [28] proposed a discrete event-triggered communication scheme, where the designed event-triggering condition only needs to be checked at every event-triggering instant. Notice that the event-triggering instant is a subset of the sampling instant, and thus the discrete event-triggered communication scheme not only reduces the network bandwidth utilization, but also saves the computation cost of the smart sensor in NCSs. Nevertheless, the above latest results still leave much room for improvement: (i) the main focus of related studies is on continuoustime linear NCSs (see [22, 23] and references therein), but little work has been conducted on that of event-triggering in discrete-time nonlinear NCSs setting; (ii) most of the existing results are based on the assumption that the lower bound of the network-induced delay is zero, which may bring some conservatism to some extent [29]. Until now, there is no work that discusses how to utilize the information of the lower bound of the network-induced delay in the eventtriggered continuous-time/discrete-time nonlinear NCSs framework. Motivated by the above observations, in this paper, we focus our attention on event-triggering in nonlinear discretetime NCSs in the presence of signal transmission delay (lower bound is not equal to zero). Since fuzzy control is a simple and effective approach to study complex nonlinear systems under the framework of T-S fuzzy model an (...truncated)