Adaptive Fuzzy Control of Nonlinear in Parameters Uncertain Chaotic Systems Using Improved Speed Gradient Method |
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Authors: | Moosa Ayati |
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Affiliation: | 1. Faculty of Electrical and Computer Engineering, K.N. Toosi University of Technology, Seyed Khandan Bridge, Shariati Street, Tehran, Iran
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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. |
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