Sliding mode control for uncertain unified chaotic systems with input nonlinearity

Function Approximation-based Sliding Mode Adaptive Control for Time-varying Uncertain Nonlinear Systems

“…2005; Fang et al, 2006;Chiang et al, 2007), neural network technique (Yang & Calise, 2007;Fu & Chai, 2007;Zhou et al, 2007Tang et al, 2007 and fuzzy method (Hsu & Lin, 2005;Huang & Chen, 2006;Liu & Wang, 2007). For instance, combining a linear nominal controller with an adaptive compensator, Ruan (2007) and Hovakimyan (2006) realized the high performance stabilizing of inverted pendulum with un-modeling nonlinear dynamics.…”

“…At present, many adaptive control methods for nonlinear uncertain system whose uncertainty satisfies some conditions (Barmish & Leitmann, 1982;Chen & Huang, 1987) or the bound of uncertainty satisfies strict conditions have been developed (L. G. Wu et al, 2006;Z. J. Wu et al, 2007;Fang et al, 2006;Chiang et al, 2007). These research problems are hotspot in the control realm, and some results have been obtained through years of hard work of researchers Chen & Huang, 2005;Huang & Liao, 2006;Liang et al, 2008).…”

Global sliding mode control and application in chaotic systems

“…The reaching law (a) is presented in [15], (b) is the conventional reaching law which is wildly used in many papers, for examples in [8][9][10][11][12][13][14].…”

“…On the other hand, besides lack of robustness in the process of reaching sliding surface, high frequency oscillations of the state trajectory known as chattering phenomenon are the major disadvantages [7][8][9][10][11][12][13][14][15], how to reduce the reaching time, and the chattering is a main problem to be solved in the design of the sliding mode control. In [8], a time varying sliding surface is introduced to cut the reaching interval.…”

“…In [8], a time varying sliding surface is introduced to cut the reaching interval. In [9][10][11][12][13][14], sliding mode controllers were presented by using a conventional reaching lawṡ = −μs − ηsgn(s), μ, η > 0, a saturation function method is proposed in [7], the authors of [15] proposed a new reaching laẇ s(t) = −μs − η s −α s, μ, η > 0, 0 < α < 1, etc.…”