NDLI: A New Sum-of-Squares Design Framework for Robust Control of Polynomial Fuzzy Systems With Uncertainties

Content Provider	IEEE Xplore Digital Library
Author	Tanaka, K. Tanaka, M. Chen, Y. Wang, H.O.
Copyright Year	1993
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 semiglobal 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 nonconvex formulations with respect to polynomial Lyapunov function parameters and polynomial feedback gains. Since a typical transformation from nonconvex 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 nonconvex 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 linear matrix inequality approaches and the existing convex SOS approach.
Sponsorship	IEEE Computational Intelligence Society
Starting Page	94
Ending Page	110
Page Count	17
File Size	1138054
File Format	PDF
ISSN	10636706
Volume Number	24
Issue Number	1
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2016-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Polynomials Robustness Fuzzy systems Lyapunov methods Uncertainty Stability analysis Robust control sum of squares copositivity polynomial Lyapunov function polynomial fuzzy system with uncertainty robust stabilization
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Artificial Intelligence Control and Systems Engineering Computational Theory and Mathematics

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