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Reliable Guaranteed Cost Control of Uncertain Systems with Nonlinear Perturbations

Received: 10 October 2020     Accepted: 23 October 2020     Published: 4 November 2020
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Abstract

Network control system (NCS) is a distributed real-time feedback control system with the continuous development of network technology. It is generally composed of network, controller, actuator and sensor. It has brought great convenience to people in many fields, but it also has many problems, which makes the research of control system more complicated. Recently, there have been some efforts to tackle the reliable guaranteed cost controller design problem, and some good results have also been obtained for the continuous-time and for the discrete-time. However, there have been few results in the literature of an investigation for the reliable guaranteed cost controller design of nonlinear uncertain systems with time-varying state delay and actuator failure. This paper concerns the reliable guaranteed cost control problem of uncertain systems with time-varying state delay and nonlinear perturbations for a given quadratic cost function. The problem is to design a reliable guaranteed cost state feedback control law which can tolerate actuator failures, such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound. Firstly, the existence condition of reliable guaranteed cost control law is given by constructing Lyapunov stability function and using linear matrix inequality (LMI). Secondly, the design method of the optimal reliable guaranteed cost controller is given by solving the convex optimization problem with LMI constraints, which minimizes the upper bound of guaranteed cost for closed-loop systems. In the end, the numerical simulation result illustrates the effectiveness of the proposed method.

Published in Advances in Applied Sciences (Volume 5, Issue 4)
DOI 10.11648/j.aas.20200504.12
Page(s) 103-111
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2020. Published by Science Publishing Group

Keywords

Reliable Control, Guaranteed Cost Control, Time-delay, Actuator Failure, LMI

References
[1] W. P. Lu, H. D. Xu, S. Y. Li, et al. Reliable guaranteed cost Control for uncertain time-lag systems of actuator failures [J]. Key Engineering Materials, 2010, 930: 960-965.
[2] I. Petersen, D. McFarlane. Optimal guaranteed cost control and filtering for uncertain linear systems [J]. IEEE Trans. Automat. Control, 1994, 39 (9): 1971-1977.
[3] N. Xie, G. Y. Tang, Delay-dependent nonfragile guaranteed cost control for nonlinear time-delay systems [J]. Nonlinear Analysis, 2006, 64 (9): 2084-2097.
[4] L. Yu, F. Gao, Optimal guaranteed cost control of discrete-time uncertain systems with both state and input delays [J]. Journal of the Franklin Institute, 2001, 338 (1): 101-110.
[5] Y. G. Kao, J. Xie, C. H. Wang. A sliding mode approach to H∞ non-fragile observer-based control design for uncertain markovian neutral-type stochastic systems [J]. Automation, 2015, 52: 218-226.
[6] Z. P. Yin, K. Yu, Y. Wang. Robust control algorithm and simulation of networked control systems. Computer Communications, 2020, 157: 394-401.
[7] Q. X. Zhu, K. H. Lu, Y. H. Zhu, S. S. Hu. The guaranteed-cost controller design for networked-control system with markov delay [J]. Aerospace Control, 2014, 32 (04): 3-7.
[8] J. Song. Fault-Tolerant control of networked control systems with time-varying actuator fault [J]. Aerospace Control, 2016, 34 (05): 3-8.
[9] X. Z. Liu. Research on fault toleran control of networked control systems [D]. Beijing institute of technology, 2016.
[10] Q. Zhu, K. Lu, G. M. Xie, et al. Guaranteed cost fault-tolerant control for networked control systems with sensor faults [J]. Mathematical Problems in Engineering, 2015, 2015.
[11] P. P. Yao, X. J. Fu. Reliable guaranteed cost control for a class of nonlinear uncertain time-delay systems [J]. Computing Technology and Automation, 2017, 36 (01): 1-5.
[12] S. Deng, L. C. Yang. Reliable H∞ control design of discrete-time Takagi-Sugeno fuzzy systems with actuator faults [J]. Neurocomputing, 2016, 173 (3): 1784-1788.
[13] J. S. Zhang, Y. W. Wang, J. W. Xiao, et al. Robust reliable guaranteed cost control of positive interval systems with multiple time delays and actuator failure [J]. International Journal of Systems Science, 2016, 47 (4): 946-955.
[14] Q. X. Zhu, K. H. Lu, Y. H. Zhu. Guaranteed cost fault-tolerant control of double-fault networked control systems: piecewise delay method [J]. Mathematical Problems in Engineering, 2019, (9): 1-19.
[15] S. X. SUN, et al. Reliable H∞ guaranteed cost control for uncertain switched fuzzy stochastic systems with multiple time-varying delays and intermittent actuator and sensor faults. Neural Computing and Applications, 2020, (4): 1-23.
[16] S. Q. Zou, H. Yan, L. Zhang. Reliable static output feedback guaranteed cost control for uncertain systems with time-delay [C]. In: Chinese Intelligent Automation Conference. Springer, Singapore, 2017, 458: 407-413.
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Cite This Article
  • APA Style

    Nana Wang, Nan Xie. (2020). Reliable Guaranteed Cost Control of Uncertain Systems with Nonlinear Perturbations. Advances in Applied Sciences, 5(4), 103-111. https://doi.org/10.11648/j.aas.20200504.12

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    ACS Style

    Nana Wang; Nan Xie. Reliable Guaranteed Cost Control of Uncertain Systems with Nonlinear Perturbations. Adv. Appl. Sci. 2020, 5(4), 103-111. doi: 10.11648/j.aas.20200504.12

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    AMA Style

    Nana Wang, Nan Xie. Reliable Guaranteed Cost Control of Uncertain Systems with Nonlinear Perturbations. Adv Appl Sci. 2020;5(4):103-111. doi: 10.11648/j.aas.20200504.12

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  • @article{10.11648/j.aas.20200504.12,
      author = {Nana Wang and Nan Xie},
      title = {Reliable Guaranteed Cost Control of Uncertain Systems with Nonlinear Perturbations},
      journal = {Advances in Applied Sciences},
      volume = {5},
      number = {4},
      pages = {103-111},
      doi = {10.11648/j.aas.20200504.12},
      url = {https://doi.org/10.11648/j.aas.20200504.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.aas.20200504.12},
      abstract = {Network control system (NCS) is a distributed real-time feedback control system with the continuous development of network technology. It is generally composed of network, controller, actuator and sensor. It has brought great convenience to people in many fields, but it also has many problems, which makes the research of control system more complicated. Recently, there have been some efforts to tackle the reliable guaranteed cost controller design problem, and some good results have also been obtained for the continuous-time and for the discrete-time. However, there have been few results in the literature of an investigation for the reliable guaranteed cost controller design of nonlinear uncertain systems with time-varying state delay and actuator failure. This paper concerns the reliable guaranteed cost control problem of uncertain systems with time-varying state delay and nonlinear perturbations for a given quadratic cost function. The problem is to design a reliable guaranteed cost state feedback control law which can tolerate actuator failures, such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound. Firstly, the existence condition of reliable guaranteed cost control law is given by constructing Lyapunov stability function and using linear matrix inequality (LMI). Secondly, the design method of the optimal reliable guaranteed cost controller is given by solving the convex optimization problem with LMI constraints, which minimizes the upper bound of guaranteed cost for closed-loop systems. In the end, the numerical simulation result illustrates the effectiveness of the proposed method.},
     year = {2020}
    }
    

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  • TY  - JOUR
    T1  - Reliable Guaranteed Cost Control of Uncertain Systems with Nonlinear Perturbations
    AU  - Nana Wang
    AU  - Nan Xie
    Y1  - 2020/11/04
    PY  - 2020
    N1  - https://doi.org/10.11648/j.aas.20200504.12
    DO  - 10.11648/j.aas.20200504.12
    T2  - Advances in Applied Sciences
    JF  - Advances in Applied Sciences
    JO  - Advances in Applied Sciences
    SP  - 103
    EP  - 111
    PB  - Science Publishing Group
    SN  - 2575-1514
    UR  - https://doi.org/10.11648/j.aas.20200504.12
    AB  - Network control system (NCS) is a distributed real-time feedback control system with the continuous development of network technology. It is generally composed of network, controller, actuator and sensor. It has brought great convenience to people in many fields, but it also has many problems, which makes the research of control system more complicated. Recently, there have been some efforts to tackle the reliable guaranteed cost controller design problem, and some good results have also been obtained for the continuous-time and for the discrete-time. However, there have been few results in the literature of an investigation for the reliable guaranteed cost controller design of nonlinear uncertain systems with time-varying state delay and actuator failure. This paper concerns the reliable guaranteed cost control problem of uncertain systems with time-varying state delay and nonlinear perturbations for a given quadratic cost function. The problem is to design a reliable guaranteed cost state feedback control law which can tolerate actuator failures, such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound. Firstly, the existence condition of reliable guaranteed cost control law is given by constructing Lyapunov stability function and using linear matrix inequality (LMI). Secondly, the design method of the optimal reliable guaranteed cost controller is given by solving the convex optimization problem with LMI constraints, which minimizes the upper bound of guaranteed cost for closed-loop systems. In the end, the numerical simulation result illustrates the effectiveness of the proposed method.
    VL  - 5
    IS  - 4
    ER  - 

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Author Information
  • College of Computer Science and Technology, Shandong University of Technology, Zibo, China

  • College of Computer Science and Technology, Shandong University of Technology, Zibo, China

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