Backstepping-based Fuzzy Adaptive Output-feedback Fault-tolerant Control For Nonlinear Systems

This article develops an adaptive fuzzy control method for accommodating actuatorfaults in a class of unknown nonlinear systems with unmeasured states. The considered faultsare modelled as both loss of effectiveness and lock-in-place (stuck at unknown place). Withthe help of fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzyadaptive observer is developed for estimating the unmeasured states. Combining thebackstepping technique with the nonlinear tolerant-fault control theory, a novel adaptive fuzzyfaults-tolerant control approach is constructed. The main contributions are as follows:(1) An adaptive fuzzy Backstepping fault-tolerant control approach is proposed for aclass of SISO uncertain nonlinear systems with actuators faults without the requirement of thestates measurement. The considered faults are modelled as both loss of effectiveness andlock-in-place (stuck at unknown place). A fuzzy state observer and a fuzzy filter are designedto estimate the unmeasured states.Then by using Backstepping control method, a fuzzyadaptive controller is constructed. Furthermore, it is proved that the proposed controlapproach can guarantee that the closed-loop system is semiglobal1y uniformly ultimatelybounded (SUUB) in probability based on the Lyapunov function theory and the tracking errorbetween the system output and the reference signal converges to a small neighbourhood ofzero by appropriate choice of the design parameters. Simulation results are provided to showthe effectiveness of the control approach.(2) An adaptive fuzzy Backstepping fault-tolerant control method is developed for aclass of uncertain MIMO nonlinear systems with actuators faults without the requirement ofthe states being available for controller design. The considered faults are modelled as bothloss of effectiveness and lock-in-place (stuck at unknown place). With the help of fuzzy logicsystems to approximate the unknown non-linear functions, a fuzzy adaptive observer isdeveloped for estimating the unmeasured states. Combining backstepping technique withnon-linear tolerant-fault control theory, a novel adaptive fuzzy fault-tolerant control approachis constructed. It is proved that the proposed control approach can guarantee that theclosed-loop system is semiglobal1y uniformly ultimately bounded (SUUB) in probabilitybased on the Lyapunov function theory the tracking errors between the system outputs and thereference signals converge to a small neighbourhood of zero. Simulation results are providedto show the effectiveness of the control approach.(3) This part investigates the adaptive fuzzy decentralized fault-tolerant control problemfor a class of nonlinear large-scale systems in strict-feedback form. The considered nonlinear system contains the unknown nonlinear functions, unmeasured states and actuator faults,which are modeled as both loss of effectiveness and lock-in-place. With the help of fuzzylogic systems to approximate the unknown nonlinear functions, and a fuzzy adaptive observeris designed to estimate the unmeasured states. By combining the backstepping technique withthe nonlinear fault-tolerant control theory, a novel adaptive fuzzy decentralized faults-tolerantcontrol (FTC) scheme is developed. It is proved that the proposed control approach canguarantee that the closed-loop system is semiglobal1y uniformly ultimately bounded (SUUB)in probability based on the Lyapunov-Krasovskii function theory the tracking error ofclosed-loop system converge to a small residual set. Simulation results are provided to showthe effectiveness of the control approach.