Stable controller design for T-S fuzzy systems based on Lie algebras

Banks S., Gurkan E., Erkmen I.

FUZZY SETS AND SYSTEMS, cilt.156, sa.2, ss.226-248, 2005 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 156 Sayı: 2
  • Basım Tarihi: 2005
  • Doi Numarası: 10.1016/j.fss.2005.05.003
  • Dergi Adı: FUZZY SETS AND SYSTEMS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.226-248
  • Anahtar Kelimeler: fuzzy systems, stability, Lie algebras, flexible-joint robot arm, STABILITY ANALYSIS, NONLINEAR-SYSTEMS, MODELS
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

In this paper, we study the stability of fuzzy control systems of Takagi-Sugeno-(T-S) type based on the classical theory of Lie algebras. T-S fuzzy systems are used to model nonlinear systems as a set of rules with consequents of the type x(t) = A(l)x (t) + B(l)u (t). We conduct the stability analysis of such T-S fuzzy models using the Lie algebra LA generated by the A(l) matrices of these subsystems for each rule in the rule base. We first develop our approach of stability analysis for a commuting algebra L-A, where all the consequent state matrices A(l)'s commute. We then generalize our results to the noncommuting case. The basic idea here is to approximate the noncommuting Lie algebra with a commuting one, such that the approximation error is minimum. The results of this approximation are extended to the most general case using the Levi decomposition of Lie algebras. The theory is applied to the control of a flexible-joint robot arm, where we also present the decomposition procedure. (c) 2005 Elsevier B.V. All rights reserved.