Adaptive sliding mode control of uncertain chaotic systems with input nonlinearity

Liu, Leipo; Pu, Jiexin; Song, Xiaona; Fu, Zhumu; Wang, Xiaohong

doi:10.1007/s11071-013-1163-6

Cited by 42 publications

(41 citation statements)

References 26 publications

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“…In the literature [12,16,17,30], the input nonlinearity of control was indicated to cause a serious degradation of system performance, unpredictable and undesirable behaviors and a reduced rate of system response. Therefore, Assumption 4 is widely used in many studies [10,12,14,16,17,22,27] for controlling uncertain chaotic systems subjected to input nonlinearity.…”

Section: Remarkmentioning

confidence: 99%

“…The design parameterη 2 in (24) is the estimate of η 2 , and η 2 is expressed as (26) where v(t) = (G 1 B) −1 (σ 1 +η 1 )sgn(s 1 (t)) (27) σ 1 > 0 and the sign function sgn(s 1 (t)) [57] is defined as…”

Section: Theorem 2 Consider the Uncertain Time-delay Chaotic System mentioning

confidence: 99%

“…Since chaos control problem was firstly considered by [6], the stabilization of chaotic systems has been paid much attention and various control strategies have been applied to realize chaos control and synchronization such as adaptive control [7][8][9][10][11][12][13][14][15], sliding mode control [2,[16][17][18][19][20][21][22][23][24][25][26][27][28][29][30], fuzzy control [31,32], linear feedback control [33,34], polynomial approach [35] and harmonic approach [36][37][38][39]. In addition, several design methods [40][41][42][43][44][45] for the stabilization of systems with uncertainties have been investigated.…”

Section: Introductionmentioning

confidence: 99%

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Chaotic sliding mode controllers for uncertain time-delay chaotic systems with input nonlinearity

Pai

2015

Applied Mathematics and Computation

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Section: Remarkmentioning

confidence: 99%

Section: Theorem 2 Consider the Uncertain Time-delay Chaotic System mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Chaotic sliding mode controllers for uncertain time-delay chaotic systems with input nonlinearity

Pai

2015

Applied Mathematics and Computation

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“…So, their effects cannot be ignored in analysis design. In recent years, much attention has been paid to the input nonlinearity [24][25][26][27][28][29], but, to the best of our knowledge, the problems of (SMC) for switched descriptor systems subjected to time-varying delay and input nonlinearity have not been fully investigated and still remain open and challenging. This has motivated the present study compiled in this paper.…”

Section: Introductionmentioning

confidence: 99%

Robust H∞ Control for Nonlinear Uncertain Switched Descriptor Systems with Time Delay and Nonlinear Input: A Sliding Mode Approach

Kchaou

Ahmadi

2017

Complexity

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This paper addresses the problem of sliding mode control (SMC) design for a class of uncertain switched descriptor systems with state delay and nonlinear input. An integral sliding function is designed and an adaptive sliding mode controller for the reaching motion is then synthesised such that the trajectories of the resulting closed-loop system can be driven onto a prescribed sliding surface and maintained there for all subsequent times. Moreover, based on a new Lyapunov-Krasovskii functional, a delaydependent sufficient condition is established such that the admissibility as well as the ∞ performance requirement of the sliding mode dynamics can be guaranteed in the presence of time delay, external disturbances, and nonlinear input which comprises dead-zones and/or sector nonlinearities. The major contributions of this paper of this approach include (i) the closed-loop system exhibiting strong robustness against nonlinear dynamics and (ii) the control scheme enjoying the chattering-free characteristic. Finally, two representative examples are given to illustrate the theoretical developments.

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“…The prominent characteristic of a chaotic system is its extreme sensitivity to initial conditions and the system's parameters. Over the past decades, chaos control has been widely investigated and many researches have been studied in this field [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. In [1], a linear feedback control method is proposed for controlling uncertain L€ u system.…”

Section: Introductionmentioning

confidence: 99%

Chaos control of uncertain time‐delay chaotic systems with input dead‐zone nonlinearity

Pai

2014

Complexity

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This article presents an adaptive sliding mode control (SMC) scheme for the stabilization problem of uncertain time-delay chaotic systems with input dead-zone nonlinearity. The algorithm is based on SMC, adaptive control, and linear matrix inequality technique. Using Lyapunov stability theorem, the proposed control scheme guarantees the stability of overall closed-loop uncertain time-delay chaotic system with input dead-zone nonlinearity. It is shown that the state trajectories converge to zero asymptotically in the presence of input dead-zone nonlinearity, time-delays, nonlinear real-valued functions, parameter uncertainties, and external disturbances simultaneously. The selection of sliding surface and the design of control law are two important issues, which have been addressed. Moreover, the knowledge of upper bound of uncertainties is not required. The reaching phase and chattering phenomenon are eliminated. Simulation results demonstrate the effectiveness and robustness of the proposed scheme.

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Adaptive sliding mode control of uncertain chaotic systems with input nonlinearity

Cited by 42 publications

References 26 publications

Chaotic sliding mode controllers for uncertain time-delay chaotic systems with input nonlinearity

Chaotic sliding mode controllers for uncertain time-delay chaotic systems with input nonlinearity

Robust H∞ Control for Nonlinear Uncertain Switched Descriptor Systems with Time Delay and Nonlinear Input: A Sliding Mode Approach

Chaos control of uncertain time‐delay chaotic systems with input dead‐zone nonlinearity

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