Paper Info
Title
Path-Following-Based Design For Guaranteed Cost Control Of Polynomial Fuzzy Systems
Abstract
This paper presents a path-following-based design for guaranteed cost control of a class of nonlinear systems represented by polynomial fuzzy systems. First, this paper proposes a polynomial Lyapunov function approach to guaranteed cost control for the feedback system consisting of a polynomial fuzzy system and a polynomial fuzzy controller. In particular, we introduce a new type of polynomial fuzzy controllers based on an approximate solution for the Hamilton-Jacobi-Bellman inequality. To design a guaranteed cost polynomial fuzzy controller effectively, a path-following-based design algorithm is newly developed by formulating as a sum-ofsquares (SOS) stabilization problem. Two new relaxations are provided by bringing a peculiar benefit of the SOS framework. One is an S-procedure relaxation for the considered outmost Lyapunov function level set that is contractively invariant set. The other is an S-procedure relaxation for design conditions obtained for polynomial membership functions redefined by variable replacements in considered ranges. Furthermore, this paper provides a practical and reasonable way for estimating lower upperbounds of a given performance function by increasing the order of a considered polynomial function. Finally, a complicated nonlinear system design example is employed to illustrate the validity of the proposed design algorithm and the lower upper-bound estimation.
Year
DOI
Venue
2021
10.1007/s40815-020-00931-9
INTERNATIONAL JOURNAL OF FUZZY SYSTEMS
Keywords
DocType
Volume
Guaranteed cost control, Hamilton-JacobiBellman inequality, Lower upper-bound estimation, Path-following-based design, Polynomial Lyapunov function, S-procedure, Sum-of-squares
Journal
23
Issue
ISSN
Citations 
1
1562-2479
1
PageRank 
References 
Authors
0.35
0
3
Name
Order
Citations
PageRank
Kai-Yi Wong110.35
Motoyasu Tanaka218025.20
Kazuo Tanaka340840.44