Fault-Tolerant Fuzzy-Resilient Control for Fractional-Order Stochastic Underactuated System With Unmodeled Dynamics and Actuator Saturation

This article is considered on underactuated fractional-order stochastic systems (FOSSs) with actuator saturation and incrementally conic nonlinear terms, whose fractional-order alpha is an element of (0, 1). First, to bring FO dynamic signals, solving the unmodeled dynamics, in the meantime, the saturated nonlinear term of the control input is taken into account. At the time, to cope with the stability issue of FOSS under such situation, the fault tolerant resilient controller based on underactuated condition is designed. Then, according to the method of the Lyapunov and Ito differential formulation to design proper multiple Lyapunov-Krasovskii (L-K) functions, such that, a novel sufficient condition of the robustly asymptotically stability of fuzzy FOSS under underactuated conditions is rigorously proved in terms of linear matrix inequality (LMI). Furthermore, in order to research the mean square stability of the above-mentioned system, so the solution of FOSS is obtained to achieve this purpose. By applying the above method, which is proposed in this work that the controlled system can be obtained with faster response and higher control accuracy. At last, to display the superiority of the above-mentioned scheme is effective, tethered satellite system and numerical results are presented.

Automated summary

This article focuses on underactuated fractional-order stochastic systems (FOSSs) with actuator saturation and incrementally conic nonlinear terms. It proposes a fault tolerant resilient controller based on underactuated conditions to address the stability issue of FOSS in the presence of unmodeled dynamics and saturated nonlinear terms. The robust asymptotic stability of fuzzy FOSS is rigorously proved using Lyapunov-Krasovskii (L-K) functions and linear matrix inequalities (LMIs). The mean square stability of the system is also investigated and numerical results are presented to demonstrate the effectiveness of the proposed scheme.