Adaptive fuzzy sliding mode control for underactuated systems with time-varying sensor faults

ABSTRACT

The tracking control problem of a class of underactuated systems that have time-varying additive and multiplicative sensor faults is studied in this paper. A composite sliding mode surface is established, and the fuzzy logic system is used to estimate the unknown term in the system. The impact of sensor faults can be counteracted by using the proposed method, which also guarantees the tracking errors converge to zero and the signals in the closed-loop system are bounded. Furthermore, the usefulness of the designed control strategy is certified via a numerical simulation.

CO EDITOR-IN-CHIEF:

• Kuo, Cheng-Chien

ASSOCIATE EDITOR:

• Su, Shun-Feng

KEYWORDS:

• Underactuated systems
• sensor faults
• sliding mode control
• fuzzy logic systems

Nomenclature

a(t)	=	The multiplicative sensor faults
e, ė	=	The tracking errors and its derivatives
FLSs	=	Fuzzy logic systems
$f_i(\mathit{\xi })$	=	Unknown bounded smooth nonlinear functions
u	=	The system input
γ	=	The weight vector
$\hat{\gamma },\mathit{\hspace{0.17em}}\tilde{\gamma }$	=	The estimated value and estimated error of γ
v(t)	=	The additive sensor faults
$\mathit{\xi }$	=	The system states
${\xi }^m$	=	The system states subject to sensor failures
${\xi }_d$	=	The desired trajectories
$\mathit{\epsilon },\mathit{\hspace{0.17em}}\bar{\epsilon }$	=	The approximate error and its upper bounded
s1, s2 and S	=	The auxiliary functions and composite sliding form surface
$\mathit{\sigma }(\mathit{\xi })$	=	The fuzzy basis functions
$\mathit{\alpha },{\lambda }_1,\mathit{\hspace{0.17em}}{\lambda }_2,\mathit{\tau }$ k1, k2	=	Positive parameters

Acknowledgments

The authors would like to sincerely extend their appreciation to the editor in-chief, the associate editor, and the anonymous reviewers for their constructive comments which helped improve the quality and presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported in part by the China Postdoctoral Science Foundation under Grant 2022M721902, in part by Guangyue Young Scholar Innovation Team of Liaocheng University under Grant LCUGYTD2022-01 and in part by Liaocheng University Major Vertical Project Cultivation Plan Project under Grant 318062305.