Adaptive stabilization of uncertain unified chaotic systems with nonlinear input

Adaptive stabilization of uncertain unified chaotic systems with nonlinear input

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Article ID: iaor201111912
Volume: 218
Issue: 8
Start Page Number: 4260
End Page Number: 4267
Publication Date: Dec 2011
Journal: Applied Mathematics and Computation
Authors: , ,
Keywords: programming: nonlinear, optimization
Abstract:

This paper addresses the problem of adaptive stabilization of uncertain unified chaotic systems with nonlinear input in the sector form. A novel representation of nonlinear input function, that is, a linear input with bounded time‐varying coefficient, is firstly established. Then, an adaptive control scheme is proposed based on the new nonlinear input model. By using Barbalat’s lemma, the asymptotic stability of the closed‐loop system is proved in spite of system uncertainties, external disturbance and input nonlinearity. One of the advantages of the proposed design method is that the prior knowledge on the plant parameter, the bound parameters of the uncertainties and the slope parameters inside the sector nonlinearity is not required. Finally, numerical simulations are performed to verify the analytical results.

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