Passive fault-tolerant control via sliding-mode-based Lyapunov redesign

This paper presents an innovative framework for passive fault-tolerant control (FTC) based on Lyapunov redesign utilizing sliding mode controllers (SMC). The paper introduces three schemes for passive FTC design. Firstly, it advocates employing Lyapunov Redesign in FTC design with the unit SMC, resulting in a generation of a discontinuous control signal. The paper establishes novel conditions for system insensibility concerning the norm of actuator faults. To address chattering and reduce energy consumption, an alternative FTC design is proposed, leveraging a multivariable version of the super-twisting algorithm, which generates a continuous signal. Additionally, a novel methodology for gain selection is developed to ensure increased tolerance to actuator faults. Finally, a new multivariable version of the Lipschitz algorithm, based on the classical Twisting controller, is formulated and applied to passive FTC through Lyapunov redesign, promising a reduced level of chattering and energy consumption compared to the super-twisting algorithm. The efficacy of the proposed FTC schemes is illustrated through simulation examples, highlighting both their advantages and potential limitations in practical applications.