Adaptive stabilization of uncertain unified chaotic systems with nonlinear input (Q426966)

The authors consider the unified chaotic system described by the following set of differential equations NEWLINE\[NEWLINE\dot x= (25\alpha+ 10)(y- x),\quad \dot y= (28- 35\alpha)x+ (29\alpha- 1)y- xz,\quad \dot z= xy- {8+\alpha\over 3} z,NEWLINE\]NEWLINE 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.NEWLINENEWLINE An adaptive control scheme is proposed based on the new nonlinear input model. Numerical simulations are performed to verify the analytical results.