A Generalized Supertwisting Algorithm

Abstract

The work proposes a generalized supertwisting algorithm (GSTA) and its constructive design strategy. In contrast with the conventional STA, the most remarkable characteristic of the proposed method is that the discontinuous term in the conventional STA is replaced with a fractional power term, which can fundamentally improve the performance of the conventional STA. It is shown that if the fractional power in the nonsmooth term becomes −1/2, the GSTA will reduce to the conventional STA. Under the GSTA, it will be rigorously verified by taking advantage of strict Lyapunov analysis that the sliding variables can finite-time converge to an arbitrarily small region in a neighborhood of the origin by tuning the gains and the fractional power. Finally, simulation studies are provided to demonstrate the superiority of the theoretically obtained results.

Numerical algorithm for hypersonic vehicle optimal flight control

“…In other words, the iterations of Algorithm 1 are reduced by 71:5%, 56:1%, and 40:3%, respectively. Furthermore, compared with the methods presented by Vasudevan et al, 15 Mei et al, 16 and Wu et al, 17,18 Unfortunately, it is impossible to take a very large value of N because of the limitation of computer accuracy. Following that, to demonstrate the effect of N on the performance of the algorithm proposed by this paper, a sensitivity analysis for N is performed and the numerical simulation results are presented by Table 2, which shows that the CPU time is also increasing as N becomes larger.…”

“…Then, to achieve the globally optimal solution Figure 6. Simulation of the embedding method, 15,16 the improved bi-level algorithm, 17 the improved mixed-integer optimal control approach, 18 and the proposed algorithm.…”

“…The embedding method 15,16 283.4981 2.9604 The improved bi-level algorithm 17 210.1056 3.0637 The improved mixed-integer optimal control approach 18 162.8217…”

A new adaptive second‐order sliding mode controller design for nonlinear systems with multiple uncertainties

“…To achieve a better control performance, the parameters in controller (42) and adaptive laws (43) are chosen as 𝜌 = 1, a = 1, r 1 = 1, Γ = 0.5 and Γ 0 = 1.5. And the control parameter values of controller (44) are given as 𝛼 1 = 2 and 𝛼 2 = 20 to ensure that the best performance can be obtained in the two different types of simulations considered subsequently.…”

“…On the basis of reference 17, the conventional SOSM control is to design a discontinuous control input $$$ u $$$ such that the nonempty set $$$ {s}_1=\dot{s}=0 $$$ can be kept. One can observe from the existing literatures that the SOSM has been extensively studied recently, generating several representative control methods, such as twisting algorithm, 24 super‐twisting algorithm, 41 sub‐optimal algorithm 42 and generalized super‐twisting algorithm, 43 and so forth.…”