Event-based networked predictive control for networked control systems subject to two-channel delays☆
Introduction
Networked control systems (NCSs) are systems in which different components such as sensor, controller, and actuator are physically distributed over a real-time network. As is well known, the NCSs have many appealing advantages such as a lower installation and maintenance cost and a more flexible architecture [17], which have dramatically stimulated a wide real world application including the remote surgery, intelligent transportation systems, automated highway systems, unmanned aerial vehicles and mobile sensor networks [6], [11], [13]. Nevertheless, the insertion of the networks has led to certain communication constraints such as the time delays and packet dropouts, which may deteriorate the performance of the NCSs and even destabilize the system. Thus, considerable effort has been devoted to dealing with these typical issues and different analysis approaches have been reported in literatures [2], [4], [14]. Among these advanced methods, the networked predictive control (NPC) technique proposed in Liu [14] is recognized as one of the most effective approaches. To date, the NPC approach has been extensively investigated [12], [19], [21], [24], [25], [26], [27] although there are still some challenges.
On the other hand, the conventional time-triggered control (TTC) method is very popular in practice because of its simplicity in controller design and implement. However, the TTC method may cause a communication burden, particularly in case of transmission of huge data over the bandwidth-limited networks [16], [23]. In such a situation, the TTC method is gradually replaced by the event-triggered scheme (ETS), which implies that the usage of the communication networks depends on the stability or certain system properties. Some studies have been reported in the literature [3], [5], [7], [8], [9], [10], [18], [20], [22], [28], [29].
Inspired by the aforementioned issues, the aim of the present work is to investigate the event-triggered predictive control problem for the NCSs subject to two-channel time delays. Specifically, the NPC technique is employed to deal with the network-induced time delays in both S-C and C-A channels and the ETS is adopted to save limited network bandwidth. Moreover, both the augmented model and the PWL (piecewise linear) model are utilized, and sufficient conditions to ensure the asymptotic stability of the resultant closed-loop systems are obtained, respectively. It is worth mentioning that the minimum data transmission times and the maximum event-triggered intervals can be obtained by the proposed methods. Then, the main contributions of this work are summarized as follows:
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The event-based NPC approach for the NCSs is proposed to reduce the communication burden of the networks and actively compensate for the time delays in S-C and C-A channels.
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Based on two different analysis approaches in the form of augmented model and PWL model, sufficient conditions to ensure the asymptotic stability of the resultant closed-loop systems are derived, respectively.
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The effectiveness and applicability of the proposed results are demonstrated by a buck DC-DC converter example.
The rest of this paper is summarized as follows. The system description and problem formulation are given in Section 2. Main results are presented in Section 3. The effectiveness and advantages of the proposed method are illustrated by stabilizing a buck DC-DC converter system in Section 4, which is followed by the conclusions in Section 5.
Notations: the notations used throughout this work are standard. The symmetric entries in a matrix is represented by the symbol *; the 2-norm of x is denoted by ; P > 0 implies that matrix P is symmetric and positive definite; denotes the n-dimensional Euclidean space; the vector is given by ; λmin{ · } refers to the minimum eigenvalues of a matrix.
Section snippets
System description and problem formulation
The structure of the NCSs under study is shown in Fig. 1, in which the communication networks are located in both the S-C channel and C-A channel. It can be observed that the measured outputs are transmitted to the controller and then the controller transmits the information to the actuator over the shared networks.
Consider the following NCSs:where xk, uk and yk denote the system state, control input, and measured output at discrete time instant k, respectively. A, B and C
Main results
In this section, two analysis approaches including the augmented model and PWL model are given, respectively. Further, sufficient conditions are derived to guarantee the asymptotic stability of the considered NCSs.
An illustrative example
In this section, a simple buck DC-DC converter system [1], [15] is considered to show the effectiveness of the proposed method. A schematic of the buck DC-DC converter system is shown in Fig. 2. A binary signal ub depicts the turn-on and turn-off of the switch, which are controlled by a fixed-frequency pulse width modulation (PWM). In addition, R, C, L, RC, RL denote the converter load, the capacitance of the capacitor, the inductance of the inductor, the equivalent series resistance of the
Conclusion
The problem of the observer-based event-triggered networked predictive control for the NCSs subject to two-channel time delays is investigated in this paper. First, the ETSy is proposed on the sensor side. Then based on the current transmitted output measurement, the observer is constructed. Particularly, the network-induced delays in both S-C and C-A channels are compensated actively by the NPC technique. Meanwhile, the ETS is proposed again on the actuator side to further reduce the
Declaration of Interest Statement
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
CRediT authorship contribution statement
Rongni Yang: Conceptualization, Methodology, Writing - original draft, Writing - review & editing, Supervision, Validation. Yaru Yu: Software, Validation, Investigation, Writing - original draft, Formal analysis. Jian Sun: Conceptualization, Supervision. Hamid Reza Karimi: Methodology, Investigation, Formal analysis.
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2023, European Journal of ControlNeural network-based event-triggered data-driven control of disturbed nonlinear systems with quantized input
2022, Neural NetworksCitation Excerpt :However, transmitting periodically in network control systems (NCSs) inevitably puts a burden on the limited bandwidth. To relax it, event-triggered (ET) control attracts growing attention for its ability to reduce transmission frequency (Cao, Wang, Guo, Huang, & Wen, 2019; Deng, Che, & Wu, 2020; Ding & Wang, 2020; Wang, Wang, Song, Shen, & Huang, 2020; Yang, Niu, & Karimi, 2022; Yang, Yu, Sun, & Karimi, 2019; Zhang, Su, Zhang, & Tian, 2021). In the ET environment, without sacrificing desired stability and performance largely, control actions are only executed when the prescribed triggering rule is violated.
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This work was supported in part by the National Natural Science Foundation of China (61873147, 61925303), the Key Project of National Natural Science Foundation of China (61733010), the Youth ChangJiang Scholars Program, and the National Key R&D Program of China under Grant 2018YFB1700100, Young Scholars Program of Shandong University (2017WLJH27), and Youth Innovation Group Project of Shandong University (2020QNQT016), and Italian Ministry of Education, University and Research under the Project “Department of Excellence LIS4.0-Lightweight and Smart Structures for Industry 4.0”.