Abstract
The super-twisting algorithm (STA) is one of the most popular second-order sliding-mode techniques. STA can achieve finite-time convergence to a region of interest called the sliding surface while completely rejecting essentially two types of perturbations (i.e., disturbances): those that vanish toward this surface and those whose total time derivative is bounded. Existing modifications of STA can reject disturbances where the latter bound, instead of being constant, can depend on the distance to the sliding surface in some specific forms. However, a general design framework allowing for perturbations of arbitrary growth was missing and was recently provided by Disturbance-Tailored Super-Twisting (DTST). In this chapter, the main concepts, requirements, and properties involved in DTST are explained.
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Notes
- 1.
Here, it becomes clear that one of the technical assumptions mentioned is that \(\hat{\nu }_1\) should be differentiable. This is not required for the initial bound \(\tilde{\nu }_1\) and hence (11) is needed. The whole set of technical assumptions required for the construction to be well-defined is given in Sect. 4.
- 2.
for example, \(\alpha = 1/\sqrt{\lambda _{\min }(P)}\).
- 3.
for example, \(\beta = \bar{\lambda }/\lambda _{\max }(P)\).
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Haimovich, H. (2023). Generalized Super-Twisting with Robustness to Arbitrary Disturbances: Disturbance-Tailored Super-Twisting (DTST). In: Oliveira, T.R., Fridman, L., Hsu, L. (eds) Sliding-Mode Control and Variable-Structure Systems. Studies in Systems, Decision and Control, vol 490. Springer, Cham. https://doi.org/10.1007/978-3-031-37089-2_1
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