Paper Info
Title
A New Sum-of-Squares Design Framework for Robust Control of Polynomial Fuzzy Systems with Uncertainties
Abstract
This paper presents a new sum-of-squares (SOS, for brevity) design framework for robust control of polynomial fuzzy systems with uncertainties. Two kinds of robust stabilization conditions are derived in terms of SOS. One is global SOS robust stabilization conditions that guarantee the global and asymptotical stability of polynomial fuzzy control systems. The other is semi-global SOS robust stabilization conditions. The latter is available for very complicated systems that are difficult to guarantee the global and asymptotical stability of polynomial fuzzy control systems. The main feature of all the SOS robust stabilization conditions derived in this paper are to be expressed as non-convex formulations with respect to polynomial Lyapunov function parameters and polynomial feedback gains. Since a typical transformation from non-convex SOS design conditions to convex SOS design conditions often results in some conservative issues, the new design framework presented in this paper gives key ideas to avoid the conservative issues. The first key idea is that we directly solve non-convex SOS design conditions without applying the typical transformation. The second key idea is that we bring a so-called copositivity concept. These ideas provide some advantages in addition to relaxations. To solve our SOS robust stabilization conditions efficiently, we introduce a gradient algorithm formulated as a minimizing optimization problem of the upper bound of the time derivative of an SOS polynomial that can be regarded as a candidate of polynomial Lyapunov functions. Three design examples are provided to illustrate the validity and applicability of the proposed design framework. The examples demonstrate advantages of our new SOS design framework for the existing LMI approaches and the existing convex SOS approach.
Year
DOI
Venue
2016
10.1109/TFUZZ.2015.2426719
Fuzzy Systems, IEEE Transactions  
Keywords
Field
DocType
copositivity,polynomial lyapunov function,polynomial fuzzy system with uncertainty,robust stabilization,sum of squares
Lyapunov function,Mathematical optimization,Polynomial,Control theory,Robustness (computer science),Fuzzy control system,Robust control,Explained sum of squares,Optimization problem,Linear matrix inequality,Mathematics
Journal
Volume
Issue
ISSN
PP
99
1063-6706
Citations 
PageRank 
References 
18
0.67
25
Authors
4
Name
Order
Citations
PageRank
Kazuo Tanaka140840.44
Motoyasu Tanaka218025.20
Chen, Ying-Jen3352.19
Hua O Wang41139135.28