IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v146y2018icp14-26.html
   My bibliography  Save this article

Finite-time stabilization for a class of nonlinear systems via optimal control

Author

Listed:
  • Zhang, Yu
  • Feng, Zhi Guo
  • Yang, Xinsong
  • Alsaadi, Fuad E.
  • Ahmad, Bashir

Abstract

In general, finite-time stabilization techniques can always stabilize a system if control cost is not considered. Considering the fact that control cost is a very important factor in control area, we investigate finite-time stabilization problem for a class of nonlinear systems in this paper, where the control cost can also be reduced. We formulate this problem into an optimal control problem, where the control functions are optimized such that the system can be stabilized with minimum control cost. Then, the control parameterization enhancing transform and the control parameterization method are applied to solve this problem. Two numerical examples are illustrated to show the effectiveness of the proposed method.

Suggested Citation

  • Zhang, Yu & Feng, Zhi Guo & Yang, Xinsong & Alsaadi, Fuad E. & Ahmad, Bashir, 2018. "Finite-time stabilization for a class of nonlinear systems via optimal control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 146(C), pages 14-26.
  • Handle: RePEc:eee:matcom:v:146:y:2018:i:c:p:14-26
    DOI: 10.1016/j.matcom.2017.09.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475417303221
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.matcom.2017.09.003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Salarieh, Hassan & Alasty, Aria, 2008. "Adaptive chaos synchronization in Chua's systems with noisy parameters," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 233-241.
    2. Xu, Bingji & Xu, Yuan & He, Linman, 2012. "LMI-based stability analysis of impulsive high-order Hopfield-type neural networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 86(C), pages 67-77.
    3. Wang, Dan & Huang, Jialiang & Lan, Weiyao & Li, Xiaoqiang, 2009. "Neural network-based robust adaptive control of nonlinear systems with unmodeled dynamics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1745-1753.
    4. Cao, Jinde & Wang, Zidong & Sun, Yonghui, 2007. "Synchronization in an array of linearly stochastically coupled networks with time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 718-728.
    5. Botmart, Thongchai & Niamsup, Piyapong, 2007. "Adaptive control and synchronization of the perturbed Chua’s system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 75(1), pages 37-55.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Mathiyalagan, K. & Ragul, R., 2022. "Observer-based finite-time dissipativity for parabolic systems with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    2. Zhang, Wanli & Yang, Xinsong & Yang, Shiju & Alsaedi, Ahmed, 2021. "Finite-time and fixed-time bipartite synchronization of complex networks with signed graphs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 319-329.
    3. Zhou, Ya & Wan, Xiaoxiao & Huang, Chuangxia & Yang, Xinsong, 2020. "Finite-time stochastic synchronization of dynamic networks with nonlinear coupling strength via quantized intermittent control," Applied Mathematics and Computation, Elsevier, vol. 376(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Pozna, Claudiu & Troester, Fritz & Precup, Radu-Emil & Tar, József K. & Preitl, Stefan, 2009. "On the design of an obstacle avoiding trajectory: Method and simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(7), pages 2211-2226.
    2. Tseng, Jui-Pin, 2016. "A novel approach to synchronization of nonlinearly coupled network systems with delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 452(C), pages 266-280.
    3. Nguyen, Le Hoa & Hong, Keum-Shik, 2011. "Synchronization of coupled chaotic FitzHugh–Nagumo neurons via Lyapunov functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(4), pages 590-603.
    4. Zhang, Chuan & Wang, Xingyuan & Luo, Chao & Li, Junqiu & Wang, Chunpeng, 2018. "Robust outer synchronization between two nonlinear complex networks with parametric disturbances and mixed time-varying delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 251-264.
    5. Djeundam, S.R. Dtchetgnia & Filatrella, G. & Yamapi, R., 2018. "Desynchronization effects of a current-driven noisy Hindmarsh–Rose neural network," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 204-211.
    6. Xie, Qian & Si, Gangquan & Zhang, Yanbin & Yuan, Yiwei & Yao, Rui, 2016. "Finite-time synchronization and identification of complex delayed networks with Markovian jumping parameters and stochastic perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 86(C), pages 35-49.
    7. Salarieh, Hassan & Alasty, Aria, 2008. "Adaptive chaos synchronization in Chua's systems with noisy parameters," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 233-241.
    8. Zhang, Hai & Ye, Miaolin & Ye, Renyu & Cao, Jinde, 2018. "Synchronization stability of Riemann–Liouville fractional delay-coupled complex neural networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 155-165.
    9. Lee, S.H. & Park, M.J. & Kwon, O.M. & Sakthivel, R., 2016. "Master-slave synchronization for nonlinear systems via reliable control with gaussian stochastic process," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 439-459.
    10. Hu, Xiaohui & Xia, Jianwei & Wei, Yunliang & Meng, Bo & Shen, Hao, 2019. "Passivity-based state synchronization for semi-Markov jump coupled chaotic neural networks with randomly occurring time delays," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 32-41.
    11. Wan, Xiaojun & Sun, Jitao, 2011. "Adaptive–impulsive synchronization of chaotic systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(8), pages 1609-1617.
    12. Li, Wang & Dai, Haifeng & Zhao, Lingzhi & Zhao, Donghua & Sun, Yongzheng, 2023. "Noise-induced consensus of leader-following multi-agent systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 1-11.
    13. Runzi, Luo & Zhengmin, Wei, 2009. "Adaptive function projective synchronization of unified chaotic systems with uncertain parameters," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1266-1272.
    14. Hollweg, Guilherme Vieira & Evald, Paulo Jefferson Dias de Oliveira & Milbradt, Deise Maria Cirolini & Tambara, Rodrigo Varella & Gründling, Hilton Abílio, 2022. "Design of continuous-time model reference adaptive and super-twisting sliding mode controller," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 215-238.
    15. Cui, Xueke & Li, Hong-Li & Zhang, Long & Hu, Cheng & Bao, Haibo, 2023. "Complete synchronization for discrete-time fractional-order coupled neural networks with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    16. Heydari, Mahdi & Salarieh, Hassan & Behzad, Mehdi, 2011. "Stochastic chaos synchronization using Unscented Kalman–Bucy Filter and sliding mode control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(9), pages 1770-1784.
    17. Yang, Xinsong & Huang, Chuangxia & Zhu, Quanxin, 2011. "Synchronization of switched neural networks with mixed delays via impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 44(10), pages 817-826.
    18. Qing Guo & Fangyi Wan, 2017. "Complete synchronization of the global coupled dynamical network induced by Poisson noises," PLOS ONE, Public Library of Science, vol. 12(12), pages 1-11, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:146:y:2018:i:c:p:14-26. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.