IDEAS home Printed from https://ideas.repec.org/a/hin/complx/8325609.html
   My bibliography  Save this article

Sum of Squares Approach for Nonlinear Control

Author

Listed:
  • Ai-ping Pang
  • Zhen He
  • Ming-han Zhao
  • Guang-xiong Wang
  • Qin-mu Wu
  • Ze-tao Li

Abstract

A proper Hamilton-Jacobi-Isaacs (HJI) inequality must be solved in a nonlinear control problem. The sum of squares (SOS) method can now be used to solve an analytically unsolvable nonlinear problem. A HJI inequality suitable for SOS approach is derived in the paper. The SOS algorithm for solving the HJI inequality is also provided. Conservativeness of the SOS method is then discussed in the paper. The conservativeness of the SOS approach is caused by the method itself, because it is really a synthesis method over the entire state space. To reduce the conservativeness, a local design on a restricted state-space region is proposed. But the SOS approach for the local design also suffers from the conservativeness problem, because the S-procedure for solving the set-containment constraint provides only a sufficient condition. The above-mentioned sources of conservativeness are peculiar for the SOS approaches. So a proper approach must be carefully selected in the design process to get a reasonable result. A design example is also given in the paper.

Suggested Citation

  • Ai-ping Pang & Zhen He & Ming-han Zhao & Guang-xiong Wang & Qin-mu Wu & Ze-tao Li, 2018. "Sum of Squares Approach for Nonlinear Control," Complexity, Hindawi, vol. 2018, pages 1-7, December.
    • Handle: RePEc:hin:complx:8325609
    DOI: 10.1155/2018/8325609
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/8503/2018/8325609.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/8503/2018/8325609.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2018/8325609?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
    ---><---

    References listed on IDEAS

    as
    1. Quanmin Zhu & Li Liu & Weicun Zhang & Shaoyuan Li, 2018. "Control of Complex Nonlinear Dynamic Rational Systems," Complexity, Hindawi, vol. 2018, pages 1-12, June.
    Full references (including those not matched with items on IDEAS)

    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. Jianhua Zhang & Quanmin Zhu & Yang Li & Xueli Wu, 2019. "Homeomorphism Mapping Based Neural Networks for Finite Time Constraint Control of a Class of Nonaffine Pure-Feedback Nonlinear Systems," Complexity, Hindawi, vol. 2019, pages 1-11, May.

    More about this item

    Statistics

    Access and download statistics

    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:hin:complx:8325609. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    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.