Moreno, Jaime A.; Negrete, Daniel Y.; Torres-González, Victor; Fridman, Leonid Adaptive continuous twisting algorithm. (English) Zbl 1352.93063 Int. J. Control 89, No. 9, 1798-1806 (2016). Summary: In this paper, an Adaptive Continuous Twisting Algorithm (ACTA) is presented. For double integrator, ACTA produces a continuous control signal ensuring finite time convergence of the states to zero. Moreover, the control signal generated by ACTA compensates the Lipschitz perturbation in finite time, i.e. its value converges to the opposite value of the perturbation. ACTA also keeps its convergence properties, even in the case that the upper bound of the derivative of the perturbation exists, but it is unknown. Cited in 14 Documents MSC: 93C40 Adaptive control/observation systems 93C15 Control/observation systems governed by ordinary differential equations 93B12 Variable structure systems 93B40 Computational methods in systems theory (MSC2010) Keywords:sliding mode control; adaptive control PDFBibTeX XMLCite \textit{J. A. Moreno} et al., Int. J. Control 89, No. 9, 1798--1806 (2016; Zbl 1352.93063) Full Text: DOI References: [1] DOI: 10.1016/j.automatica.2012.11.042 · Zbl 1259.93033 · doi:10.1016/j.automatica.2012.11.042 [2] DOI: 10.1007/b139028 · Zbl 1078.93002 · doi:10.1007/b139028 [3] Emelyanov S.V., Soviet Journal of Computer and System Science, 24 (4) pp 63– (1986) [4] DOI: 10.1007/978-3-319-18290-2_2 · Zbl 1321.93024 · doi:10.1007/978-3-319-18290-2_2 [5] Hardy G.H., Inequalities (1951) [6] Khalil, H.K. (2002).Nonlinear systems(3rd ed., 750 p). Upper Saddle River (NJ): Prentice-Hall. · Zbl 1003.34002 [7] DOI: 10.1080/00207179308923053 · Zbl 0789.93063 · doi:10.1080/00207179308923053 [8] DOI: 10.1016/j.automatica.2012.02.024 · Zbl 1246.93028 · doi:10.1016/j.automatica.2012.02.024 [9] DOI: 10.1007/978-3-642-84379-2 · doi:10.1007/978-3-642-84379-2 [10] DOI: 10.1201/9781420065619 · doi:10.1201/9781420065619 [11] DOI: 10.1016/j.automatica.2012.09.008 · Zbl 1257.93022 · doi:10.1016/j.automatica.2012.09.008 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.