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Adaptive stabilization of uncertain unified chaotic systems with nonlinear input. (English) Zbl 1245.65076

The authors consider the unified chaotic system described by the following set of differential equations \[ \dot x= (25\alpha+ 10)(y- x),\quad \dot y= (28- 35\alpha)x+ (29\alpha- 1)y- xz,\quad \dot z= xy- {8+\alpha\over 3} z, \] where \(x\), \(y\), \(z\) are state variables and the system parameter \(\alpha\in[0,1]\). – A novel representation of nonlinear input function, that is, a linear input with bounded time-varying coefficient, is established.
An adaptive control scheme is proposed based on the new nonlinear input model. Numerical simulations are performed to verify the analytical results.

MSC:

65K10 Numerical optimization and variational techniques
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