A Novel Method to Estimate the Reaching Time of the Super-Twisting Algorithm

The super-twisting algorithm is a well-known technique in the field of sliding mode control or observation. In this contribution, an exact analytic expression for this algorithm's finite reaching time in the unperturbed case is derived. Based on this derivation, a novel estimation for the upper bound of the algorithm's reaching time the presence of perturbations is presented. The considered perturbations may be composed of additive components that are either Lipschitz continuous in time or Hölder continuous in the sliding variable. Both analytically and in the course of numerical examples the new strategy is shown to yield significant improvements compared to existing reaching time estimates.

[1]  Shouchuan Hu.  Differential equations with discontinuous right-hand sides☆ , 1991 .

[2]  Vadim I. Utkin,et al.  On Convergence Time and Disturbance Rejection of Super-Twisting Control , 2013, IEEE Transactions on Automatic Control.

[3]  Leonid M. Fridman,et al.  Optimal Lyapunov function selection for reaching time estimation of Super Twisting algorithm , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[4]  Alexander S. Poznyak,et al.  Reaching Time Estimation for “Super-Twisting” Second Order Sliding Mode Controller via Lyapunov Function Designing , 2009, IEEE Transactions on Automatic Control.

[5]  Jaime A. Moreno,et al.  Construction of Lyapunov Functions for a Class of Higher Order Sliding Modes algorithms , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[6]  Leonid M. Fridman,et al.  Saturated Super-Twisting Algorithm based on Perturbation Estimator , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[7]  Stephen P. Boyd,et al.  A bisection method for computing the H∞ norm of a transfer matrix and related problems , 1989, Math. Control. Signals Syst..

[8]  Yannick Aoustin,et al.  Finite Time Stabilization of a Perturbed Double Integrator—Part I: Continuous Sliding Mode-Based Output Feedback Synthesis , 2011, IEEE Transactions on Automatic Control.

[9]  A. Levant.  Sliding order and sliding accuracy in sliding mode control , 1993 .

[10]  J. Moreno.  Lyapunov Approach for Analysis and Design of Second Order Sliding Mode Algorithms , 2011 .

[11]  Bijnan Bandyopadhyay,et al.  Continuous output integral sliding mode control for switched linear systems , 2016 .

[12]  Silvia Spataru.  An absolutely continuous function whose inverse functionis not absolutely continuous , 2004 .

[13]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[14]  Leonid M. Fridman,et al.  Is It Reasonable to Substitute Discontinuous SMC by Continuous HOSMC? , 2017, ArXiv.

[15]  A. Levant.  Robust exact differentiation via sliding mode technique , 1998 .

[16]  Christopher Edwards,et al.  Sliding Mode Control and Observation , 2013 .

[17]  Jaime A. Moreno,et al.  Strict Lyapunov Functions for the Super-Twisting Algorithm , 2012, IEEE Transactions on Automatic Control.