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In this paper, a method for distributed control of nonlinear Burger’s equation is proposed. In this method, first the nonlinear partial differential equation governing the system is transformed into two linear partial differential equations using the Takagi-Sugeno linearization; such that their fuzzy composition exactly recovers the original nonlinear equation. This is done to alleviate the aliasing phenomenon occuring in nonlinear equations. Then, each of the two linear equations is converted to a set of ordinary differential equations using the fast Fourier transform (FFT). Thus, the combination of Takagi-Sugeno method and FFT technique leads to two ordinary differential equation for each grid point. For the stabilization of the dynamics of each grid point, the use is made of the parallel distributed compensation method. The stability of the proposed control method is proved using the second Lyapunov theorem for fuzzy systems. In order to solve the nonlinear burger equation, a combination of FFT and finite difference methodologies is implemented for the . Simulation studies show the performance of the proposed method, for example the smaller settling time and overshoot and relatively robustness with respect to the measurement noises.

Keywords: Nonlinear Burger’s equation, Takagi-Sugeno fuzzy method, Fast fourier transform, Parallel distributed compensation

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