Static Output-Feedback Tracking Control for Positive Polynomial Fuzzy Systems

Lining Fu, H. K. Lam*, Fucai Liu, Bo Xiao, Zhixiong Zhong

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)

Abstract

Nonlinear positive control system can be found in many real-world applications but the positivity requirements lead to challenges in system analysis and control design. In this article, we approach the problem by fuzzy-model-based control techniques and overcome some challenges including transforming the nonconvexity conditions when both positive and stability conditions exist into convexity conditions that can be solved by the convex programming techniques. This article focuses on the static output-feedback tracking control issue of positive polynomial fuzzy-model-based systems. The purpose of the tracking control is to design an appropriate static output feedback polynomial fuzzy controller which can drive the system states of the nonlinear plant to follow those of a stable reference model subject to an H∞ performance. The concept of imperfectly matched premises is employed to enhance the design and implementation flexibility. To circumvent the problem of nonconvex stability conditions, an approach is employed to transform the nonconvex stability conditions into convex ones by introducing a novel scalar implantation transformation technique. Besides, the partition approximation of membership functions with local information of membership functions is used to promote stability analysis and synthesis of controllers. The positive and relaxed stability conditions for static output-feedback tracking control with H∞ performance being taken into account are obtained in terms of sum-of-squares. Finally, a simulation example is presented to verify the effectiveness of the proposed tracking control approach.

Original languageEnglish
Pages (from-to)1722-1733
Number of pages12
JournalIEEE Transactions on Fuzzy Systems
Volume30
Issue number6
DOIs
Publication statusPublished - 1 Jun 2022
Externally publishedYes

Keywords

  • Hperformance
  • imperfectly matched premises
  • membership-function-dependent stability analysis
  • positive polynomial fuzzy-model-based (PPFMB)
  • scalar implantation transformation (SIT)
  • static output-feedback tracking control

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