Adaptive type-2 fuzzy backstepping control of uncertain fractional-order nonlinear systems with unknown dead-zone (Q2310555)

The paper stands between a survey and a specific contribution. There is considered the controlled system with fractional derivatives \begin{align*} D^\beta x_1 = x_2 + f_1(x_1) + \omega_1(t)\, 0<\beta<1\\ D^\beta x_2 = x_3 + f_2(x_1,x_2) + \omega_2(t)\\ \vdots\\ D^\beta x_{n-1} = x_n + f_{n-1}(x_1,\ldots,x_{n-1}) + \omega_{n-1}(t)\\ D^\beta x_n = u + f_n(x_1,\ldots,x_n) + \omega_n(t)\\ y = x_1 \end{align*} and \[ u=\begin{cases}g_r(\nu)\, & \nu\geq b \\ 0\, & -b< \nu < b \\ g_l(\nu)\, & \nu\leq b \end{cases} \] For the controller synthesis there is considered an interaction of approaches: adaptive, fuzzy and backstepping. Computer simulation results are given. The paper is endowed by an impressive list of 57 references.