Adaptive dual-layer super-twisting control and observation

Abstract

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.

State Estimation For An Agonistic‐Antagonistic Muscle System

“…The adaptive sliding mode observer for our system is designed based on the dual layer nested adaptive approaches in [13,14]. The proposed adaptive sliding mode observer is given as follows:…”

Development and evaluation of an integral sliding mode fault‐tolerant control scheme on the RECONFIGURE benchmark

“…For details, see the work of Nagesh and Edwards. 52 If the bounds on the uncertainty exist but are not known, it is also possible to incorporate an adaptive super-twisting structure 54,55 to replace the structure in Equation 29.…”

A simplified version of adaptive super‐twisting control

“…Several controllers with adaptive gains based on the Lyapunov function have been proposed . The approach in the work of Dávila et al and Shtessel et al allows driving to zero the sliding variable in the presence of the disturbances/uncertainties; however, the adaptive gain is overestimated.…”

“…1,4 However, the resulting gains are overestimated and induce a large (versus the current uncertainties and perturbations) control effort increasing the chattering effect, which is one of the reasons for the development of adaptive gains.Several controllers with adaptive gains based on the Lyapunov function have been proposed. [6][7][8][9][10] The approach in the work of Dávila et al 6 and Shtessel et al 7 allows driving to zero the sliding variable in the presence of the disturbances/uncertainties; however, the adaptive gain is overestimated. An approach based on decreasing the gain when the sliding variable tends to zero, it has been developed in the work of Shtessel et al 8,9 and Haghighi and Mobayen 11 to overcome this problem.…”

“…[6][7][8][9][10] The approach in the work of Dávila et al 6 and Shtessel et al 7 allows driving to zero the sliding variable in the presence of the disturbances/uncertainties; however, the adaptive gain is overestimated. An approach based on decreasing the gain when the sliding variable tends to zero, it has been developed in the work of Shtessel et al 8,9 and Haghighi and Mobayen 11 to overcome this problem. Nevertheless, these control strategies require numerous gains/parameters, and the selection of their 5704…”