NDLI: Adaptive Fuzzy Control of Nonlinear in Parameters Uncertain Chaotic Systems Using Improved Speed Gradient Method

Content Provider	Springer Nature Link
Author	Ayati, Moosa
Copyright Year	2011
Abstract	This paper presents an adaptive fuzzy controller for Nonlinear in Parameters (NLP) chaotic systems with parametric uncertainties. In the proposed controller, the unknown parameters are estimated by the novel Improved Speed Gradient (ISG) method, which is a modification of Speed Gradient (SG) algorithm. ISG employs the Lagrangian of two suitable objective functionals for on-line estimation of system parameters. The most significant advantage of ISG is that it is applicable to NLP systems and it results in a faster rate of convergence for the estimated parameters than the SG method. Estimated parameters are used to design the fuzzy controller and to calculate the Lyapunov exponents of the chaotic system adaptively. Furthermore, established on the well-known Takagi–Sugeno (T-S) fuzzy model, a LMI (Linear Matrix Inequality)-based fuzzy controller is designed and is tuned using estimated parameters and Lyapunov exponents. Throughout the controller design procedure, several important issues in fuzzy control theory including relaxed stability analysis, control input performance specifications, and optimality are taken into account. Combination of ISG parameter estimation method and T-S-based fuzzy controller yields an adaptive fuzzy controller capable to suppress uncertainties in parameters and initial states of NLP chaotic systems. Finally, simulation results are provided to show the effectiveness of the ISG and adaptive fuzzy controller on chaotic Lorenz system and Duffing oscillator.
Starting Page	911
Ending Page	926
Page Count	16
File Format	PDF
ISSN	0278081X
Journal	Circuits, Systems, and Signal Processing
Volume Number	31
Issue Number	3
e-ISSN	15315878
Language	English
Publisher	SP Birkhäuser Verlag Boston
Publisher Date	2011-09-21
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Chaotic system Nonlinear in parameter system identification Lyapunov exponents Improved gradient method Takagi–Sugeno fuzzy controller Electrical Engineering Signal, Image and Speech Processing Circuits and Systems Electronics and Microelectronics, Instrumentation
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Signal Processing

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