Elsevier

Neurocomputing

Volume 338, 21 April 2019, Pages 55-62
Neurocomputing

A novel event-based fuzzy control approach for continuous-time fuzzy systems

https://doi.org/10.1016/j.neucom.2019.01.098Get rights and content

Abstract

This paper investigates the event-based fuzzy control problem for continuous-time interval type-2 (IT2) fuzzy networked control systems (NCSs). A new Lyapunov–Krasovskii functional is introduced in the stability analysis, where the integrands of the Lyapunov–Krasovskii functional are dependent of membership functions. Applying the information of time-derivatives of membership functions, a novel switching event-based fuzzy controller is designed to ensure that the closed-loop IT2 fuzzy system with mismatched membership functions is asymptotically stable. Different from the existing event-based fuzzy control results, both of the information of membership functions and the time-derivatives of membership functions can be utilized in the stability analysis to reduce the conservativeness. Finally, a simulation example is given to show the effectiveness and advantages of the design and analysis.

Introduction

The event-based control problem of networked control systems (NCSs) has been a hot research field for mitigating the unnecessary consume of network resources by applying an event-driven condition to determine when the sampled-data should be transmitted into the communication network. So far, many efficient event-triggered control/filter methodologies have been developed to reduce the utilization of limited network bandwidth [1], [2], [3], [4]. Recently, the event-based control techniques have been developed to nonlinear fuzzy NCSs, and many important achievements [5], [6], [7], [8], [9], [10] have been published. In [6], the authors first introduce the event-based fuzzy control communication scheme for T-S fuzzy NCSs. However, this paper needs to assume that the membership functions (MFs) of the investigated fuzzy system and the designed fuzzy controller are synchronous. In the authors following results, this assumed condition has been removed, and an important scheme has been proposed in [11] to solve the MFs asynchronous problem. By applying the result in [11], some related event-triggered fuzzy control/filter results have been addressed under asynchronous MFs.

However, the aforementioned event-based fuzzy control/filter results for fuzzy NCSs are all discussed under the assumption that MFs for considered fuzzy systems are without uncertainty parameter, which is strict for many nonlinear control systems [12], [13]. Compared with the fuzzy logic systems in [14], [15], [16], [17], [18], [19], [20], an IT2 fuzzy technique [12], [13] has been presented due to the advantage that the IT2 fuzzy model has excellent approximation approach to represent the nonlinear systems with uncertainties. Many important schemes [21], [22] have been considered for various fuzzy control schemes for interval type-2 fuzzy systems (IT2-FSs). As mentioned above, uncertain parameter widely exist in many practical nonlinear systems. However, most of the existing event-driven fuzzy control/filter schemes in [6], [7], [8] for fuzzy NCSs are restricted to the case of MFs without uncertain information. The control problem of the type-2 fuzzy systems has been utilized in many practice engineering fields, such as active suspension systems [23], autonomous mobile robots [24], electro hydraulic servo systems [25]. In this paper, the application scope of the event-based communication scheme has been extended in the framework of IT2 fuzzy systems, which is utilized to reduce the utilization of network resources in the practice NCSs. Thus, the event-based fuzzy control problem for IT2 NCSs is of practical significance. More recently, Pan and Yang in [26], [27] investigated the event-based fuzzy control/filter problems for nonlinear NCSs with parameter uncertain by utilizing an IT2 fuzzy approach. In [9], [10], [26], the authors addressed the problems of asynchronous premise variables and mismatched MFs by employing slack matrices technique which cannot be solved by the approach in [11] since the Lipschitz condition of mismatched MFs in [9], [10], [26] cannot be satisfied. In addition, an important fuzzy control technique for fuzzy systems has been proposed in [28]. A novel MFs dependent Lyapunov function has been utilized to reduce the conservativeness, in which the integrand in the Lyapunov function depends not only on the integral but also on the MFs. In [28], the authors have been introduced some novel techniques to handle the time-derivatives of the fuzzy Lyapunov function. However, all of the existing event-based fuzzy control/filter results mentioned above are independent of the analysis of the time-derivatives of MFs, the stability result without its information is conservative since the MFs are derivable in many fuzzy systems. For this reason, it is signicative to investigate how to utilize the information of time-derivatives of MFs in the stability analysis for event-based fuzzy NCSs.

Motivated by above insight, we propose a novel analysis approach with event-driven fuzzy control strategy for a class of continue-time IT2 fuzzy NCSs. The main contributions of this work are as follows: (1) A novel event-driven fuzzy controller design mechanism for IT2 continue-time fuzzy NCSs is presented in this paper by introducing a MFs dependent Lyapunov–Krasovskii functional which is different from the existing event-based fuzzy/filter results [9], [11], [26]. (2) Compared with the event-based fuzzy/filter results [9], [11], [26], both of the information of MFs and the time-derivatives of MFs can be utilized in the stability analysis for reducing the conservativeness. (3) Unlike the time-based fuzzy control approach for continue-time fuzzy systems [28] with constant time delays, a novel fuzzy controller design approach under event-driven strategy is proposed for general nonlinear system with uncertainties and time-varying delays.

Notation: The superscript “T” and “1” denote matrix transposition and inverse. The symbol ⋆ within a matrix is the symmetric terms, and diag{} denotes a block-diagonal matrix.

Section snippets

The IT2-FS

In this paper, consider the following nonlinear model described by IT2-FSs

Plant Rule i: IF ϕ1(x(t)) is g1i, ⋅⋅⋅, and ϕp(x(t)) is gpi,THEN:x˙(t)=Aix(t)+Biu(t)+Ciw(t),z(t)=Dix(t)+Eiu(t),where ϕp(x(t)) is the known premise variable, x(t)Rx denotes the state, w(t) ∈ L2[0, ∞) satisfying w2=t=0|w(t)|2and u(t)Ru denote the external disturbance and control input, respectively. Ai, Bi, Ci, Di, and Ei denote known matrices. Applying the IT2-FS modeling technique [21], one can have the following

Main results

In this section, the main result of the event-based closed-loop system (13) is proposed in Theorem 1 by using a new Lyapunov–Krasovskii functional and a switching controller design scheme.

Theorem 1

Given constants ϕM > 0 and εm[0,1), the closed-loop system (13) is asymptotically stable with an H performance γ > 0 if the MFs satisfy qj(x(tsh))δjhj(x(t))0 (0 < δj ≤ 1) and there exist matrices Φ > 0, Gi > 0, Ui > 0, Ni > 0 and Zi=ZiT, M1, M2, R satisfying (i,j=1,2,,r):ΘijZi<0,δiΘiiδiZi+Zi<0,δjΘij+δiΘj

Simulation example

In this section, we investigate a mass–spring–damper system to validity the effectiveness and advantages of the introduced event-based controller design strategy for IT2 fuzzy NCSs. The physical model is shown as:mx¨+Ff+Fs=u(t).Assume that Ff=cx˙ with c > 0 and Fs=β(1+a2x2)x. Then, we can have:mx¨+cx˙+βx+βa2x3=u(t).The parameters of the mass–spring–damper system are given in [26], the uncertain parameter β[4,7]. Define x(t)=[x1(t)x2(t)]=[xx˙] and Ψ(t)=ββa2x12(t)m. Then, we can have Ψmax=4

Conclusion

In this paper, an event-based state-feedback controller design problem has been developed for continue-time IT2 fuzzy NCSs. A novel event-based controller design approach has been proposed by considering a new Lyapunov–Krasovskii functional, where both of the information of the MFs and the time-derivatives of MFs can be utilized in the stability analysis. The simulation result has been given to show the advantages of the applied method. In future work, we will attempt to apply the proposed

Yingnan Pan received the B.S. degree in mathematics and applied mathematics and the M.S. degree in applied mathematics from Bohai University, Jinzhou, China, in 2012 and 2015, respectively. He is studying for the Ph.D. degree in navigation guidance and control in Northeastern University, Shenyang, China. His research interests include fuzzy control, robust control and their applications.

References (35)

  • Y. Zhang et al.

    Distributed adaptive consensus tracking control for nonlinear multi-agent systems with state constraints

    Appl. Math. Comput.

    (2018)
  • P. Tabuada

    Event-triggered real-time scheduling of stabilizing control tasks

    IEEE Trans. Autom. Control

    (2007)
  • P. Shi et al.

    Network-based event-triggered control for singular systems with quantizations

    IEEE Trans. Ind. Electron.

    (2016)
  • Y.-L. Wang et al.

    Event-triggered fault detection filter design for a continuous-time networked control system

    IEEE Trans. Cybern.

    (2016)
  • C. Peng et al.

    To transmit or not to transmit: a discrete event-triggered communication scheme for networked Takagi–Sugeno fuzzy systems

    IEEE Trans. Fuzzy Syst.

    (2013)
  • H. Li et al.

    Event-triggered fault detection of nonlinear networked systems

    IEEE Trans. Cybern.

    (2017)
  • Y. Pan et al.

    Event-triggered fault detection filter design for nonlinear networked systems

    IEEE Trans. Syst. Man Cybern. Syst.

    (2018)
  • Cited by (5)

    Yingnan Pan received the B.S. degree in mathematics and applied mathematics and the M.S. degree in applied mathematics from Bohai University, Jinzhou, China, in 2012 and 2015, respectively. He is studying for the Ph.D. degree in navigation guidance and control in Northeastern University, Shenyang, China. His research interests include fuzzy control, robust control and their applications.

    Guang-Hong Yang (SM’04) received the B.S. and M.S. degrees in Mathematics, and Ph.D. degree in control theory and control engineering with Northeast University, Shenyang, China, in 1983, 1986, and 1994, respectively. From 2001 to 2005, he was a Research Scientist/Senior Research Scientist with the Nation- al University of Singapore, Singapore. He is currently a Professor and the dean with the College of Information Science and Engineering, Northeastern University. His current research interests include fault-tolerant control, fault detection and isolation, cyber physical systems, and robust control. Dr. Yang is a Deputy Editor-in-Chief for the Journal of Control and Decision, an Editor for the International Journal of Control, Automation and Systems, and an Associate Editor for the International Journal of Systems Science, the IET Control Theory and Applications and the IEEE Transactions on Fuzzy Systems.

    This work was supported in part by the Funds of the National Natural Science Foundation of China (Grant nos. 1. 61621004 and 1. 61420106016), the Fundamental Research Funds for the Central Universities (No. N160406003), and the Research Fund of State Key Laboratory of Synthetical Automation for Process Industries (Grant no. 2018ZCX03).

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