IDEAS home Printed from https://ideas.repec.org/a/hin/complx/5124108.html
   My bibliography  Save this article

Application of Sum of Squares Method in Nonlinear H ∞ Control for Satellite Attitude Maneuvers

Author

Listed:
  • Fanwei Meng
  • Dini Wang
  • Penghui Yang
  • Guanzhou Xie

Abstract

The Hamilton–Jacobi–Issacs (HJI) inequality is the most basic relation in nonlinear H ∞ design, to which no effective analytical solution is currently available. The sum of squares (SOS) method can numerically solve nonlinear problems that are not easy to solve analytically, but it still cannot solve HJI inequalities directly. In this paper, an HJI inequality suitable for SOS is firstly derived to solve the problem of nonconvex optimization. Then, the problems of SOS in nonlinear H ∞ design are analyzed in detail. Finally, a two-step iterative design method for solving nonlinear H ∞ control is presented. The first step is to design an adjustable nonlinear state feedback of the gain array of the system using SOS. The second step is to solve the L 2 gain of the system; the optimization problem is solved by a graphical analytical method. In the iterative design, a diagonally dominant design idea is proposed to reduce the numerical error of SOS. The nonlinear H ∞ control design of a polynomial system for large satellite attitude maneuvers is taken as our example. Simulation results show that the SOS method is comparable to the LMI method used for linear systems, and it is expected to find a broad range of applications in the analysis and design of nonlinear systems.

Suggested Citation

  • Fanwei Meng & Dini Wang & Penghui Yang & Guanzhou Xie, 2019. "Application of Sum of Squares Method in Nonlinear H ∞ Control for Satellite Attitude Maneuvers," Complexity, Hindawi, vol. 2019, pages 1-10, November.
    • Handle: RePEc:hin:complx:5124108
    DOI: 10.1155/2019/5124108
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/8503/2019/5124108.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/8503/2019/5124108.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2019/5124108?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
    ---><---

    Citations

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


    Cited by:

    1. Ruijuan Li & Onur Alp İlhan & Jalil Manafian & Khaled H. Mahmoud & Mostafa Abotaleb & Ammar Kadi, 2022. "A Mathematical Study of the (3+1)-D Variable Coefficients Generalized Shallow Water Wave Equation with Its Application in the Interaction between the Lump and Soliton Solutions," Mathematics, MDPI, vol. 10(17), pages 1-17, August.
    2. khabaz, Mohamad Khaje & Eftekhari, S. Ali & Toghraie, Davood, 2022. "Vibration and dynamic analysis of a cantilever sandwich microbeam integrated with piezoelectric layers based on strain gradient theory and surface effects," Applied Mathematics and Computation, Elsevier, vol. 419(C).
    3. Mohammed Balubaid & Osman Taylan & Mustafa Tahsin Yilmaz & Ehsan Eftekhari-Zadeh & Ehsan Nazemi & Mohammed Alamoudi, 2022. "Central Nervous System: Overall Considerations Based on Hardware Realization of Digital Spiking Silicon Neurons (DSSNs) and Synaptic Coupling," Mathematics, MDPI, vol. 10(6), pages 1-20, March.
    4. Man-Wen Tian & Shu-Rong Yan & Jinping Liu & Khalid A. Alattas & Ardashir Mohammadzadeh & Mai The Vu, 2022. "A New Type-3 Fuzzy Logic Approach for Chaotic Systems: Robust Learning Algorithm," Mathematics, MDPI, vol. 10(15), pages 1-20, July.

    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:5124108. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.