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access icon free Discrete polynomial fuzzy systems control

  • Author(s): Ying-Jen Chen 1 ; Motoyasu Tanaka 1 ; Kazuo Tanaka 1 ; Hiroshi Ohtake 2 ; Hua O. Wang 3
    • View affiliations
    • Affiliations: 1: Department of Mechanical Engineering and Intelligent Systems, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu, Tokyo 182-8585, Japan;
      2: Department of Mechanical Information Science and Technology, Kyushu Institute of Technology, 680-4 Kawazu Iizuka-City, Fukuoka 820-8502, Japan;
      3: Department of Mechanical Engineering, Boston University, 110 Cummington Street, Boston, MA 02215, USA
  • Source: Volume 8, Issue 4, 06 March 2014, p. 288 – 296
    DOI:  10.1049/iet-cta.2013.0645 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Received 12/07/2013, Accepted 23/10/2013, Revised 12/09/2013, Published 06/02/2014

This study presents a sum-of-squares (SOS) approach to stable control and guaranteed cost control of discrete polynomial fuzzy systems. The SOS framework presented in this paper offers a new paradigm over the existing linear matrix inequality (LMI) approaches to discrete Takagi–Sugeno (T–S) fuzzy models. At first, this study, newly introduces a discrete polynomial fuzzy model that is more general and effective than the well-known discrete T–S fuzzy model. With considering the operating domain, stable control design conditions are then derived based on state-dependent Lyapunov functions that contain quadratic Lyapunov functions as a special case. Hence, the design approach discussed in this study could be more general than the LMI design approaches based on quadratic Lyapunov functions. Moreover, this study also discusses a guaranteed cost control design which is carried out by minimising the upper bound of a given performance function. All the design conditions derived in this study can be represented in terms of SOS and are symbolically and numerically solved via the SOSOPT and the SeDuMi, respectively. Finally, the ball-and-beam system is provided as an example to illustrate the utility of the proposed SOS-based design approach.

Inspec keywords: Lyapunov methods; polynomials; fuzzy systems; cost optimal control; discrete systems; linear matrix inequalities; fuzzy control; stability; control system synthesis

Other keywords: SOSOPT; ball-and-beam system; SOS framework; linear matrix inequality approaches; stable control design conditions; discrete polynomial fuzzy systems control; sum-of-squares approach; guaranteed cost control design; LMI; discrete Takagi-Sugeno fuzzy models; T-S fuzzy models; quadratic Lyapunov functions; SeDuMi; state-dependent Lyapunov functions

Subjects: Stability in control theory; Discrete control systems; Linear algebra (numerical analysis); Control system analysis and synthesis methods; Fuzzy control; Optimal control

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