Adaptation of sliding modes

Bartolini, G.; Levant, Arie; Plestan, Franck; Taleb, Mohammed; Punta, Elisabetta

doi:10.1093/imamci/dns019

Cited by 68 publications

(42 citation statements)

References 9 publications

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“…Furthermore in certain engineering circumstances, see for example Alwi and Edwards (2013), the disturbance f (t) can have quite different characteristics at different periods of time, requiring very different gain levels. This has motivated the development of adaptive (secondorder) sliding mode strategies (Plestan et al 2010, Alwi and Edwards 2013, Shtessel et al 2012, Bartolini et al 2013. In certain situations it is very desirable to allow the gains α andβ to be functions of time and to increase or decrease as appropriate.…”

Section: Introductionmentioning

confidence: 99%

“…If tight time varying bounds on the uncertainty are available and known, the approach in Gonzalez et al (2012) can be adopted. However if such bounds are not available or are conservative, adaptive approaches such as those proposed in (Plestan et al 2010, Alwi and Edwards 2013, Shtessel et al 2012, Bartolini et al 2013) must be employed. This problem is considered in this paper and in the following sections.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive dual-layer super-twisting control and observation

Edwards

Shtessel

2016

International Journal of Control

119

174

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In this paper a super-twisting-like structure with adaptive gains is proposed. The structure is parameterized by two scalar gains, both of which adapt, and by an additional time-varying term. The magnitudes of the adaptive terms are allowed to both increase and decrease as appropriate so that they are as small as possible, in the sense that they do not unnecessarily over-bound the uncertainty, and yet are large enough to sustain a sliding motion. In the paper, a new time varying gain is incorporated into the traditional super-twisting architecture. The proposed adaption law has a dual-layer structure which is formally analyzed using Lyapunov techniques. The additional term has the effect of simplifying the stability analysis whilst guaranteeing the second order sliding mode properties of the traditional super-twisting scheme.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Adaptive dual-layer super-twisting control and observation

Edwards

Shtessel

2016

International Journal of Control

119

174

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“…where d̄1 ≥ 0 is some known upper bound for the disturbance d 1 (x, t), satisfying inequality (4). From (14), the disturbance d(t) in Equation (7) is given by the sum…”

Section: Modulation Function For Output-feedback Uvcmentioning

confidence: 99%

Adaptive unit vector control of multivariable systems using monitoring functions

Hsu

Oliveira

Cunha

et al. 2018

Intl J Robust & Nonlinear

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Summary An adaptive sliding‐mode unit vector control approach based on monitoring functions to deal with disturbances of unknown bounds is proposed. An uncertain multivariable linear system is considered with a quite general class of nonsmooth disturbances. Global stabilization/tracking is demonstrated using either state or output feedback. The proposed adaptation method makes the control gain less conservative, becoming large enough when the disturbance grows and becoming smaller when it decreases, leading to reduced chattering effects. In contrast to previous methods, the new switching scheme is able to guarantee a prespecified transient time, maximum overshoot, and steady‐state error for multivariable uncertain plants. The proposed technique is applied to the trajectory tracking control of a surface vessel subjected to ocean currents, wind, and waves. Simulations are presented to show the performance of the new adaptation scheme in this adverse scenario of possibly growing, temporarily large, or vanishing exogenous disturbances.

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“…From these considerations, in this paper, under unknown input, a second sliding mode differentiator making the parameter α variable according to the noise is proposed. Note that adaptive schemes of sliding mode controllers exist in the literature ( [15], [16], [17], [21], [22], [23], [24], [25], [26], [27]) but to our best of knowledge, there is no results yet in the literature dealing with a variable exponent of higher order sliding mode differentiators schemes. For schemes of differentiators with variables gains, see the works of [2] and [11].…”

Section: Introductionmentioning

confidence: 99%