Barrier Lyapunov function-based fixed-time FTC for high-order nonlinear systems with predefined tracking accuracy

Abstract

This article proposes a fixed-time adaptive fault-tolerant control methodology for a larger class of high-order (powers are positive odd integers) nonlinear systems subject to asymmetric time-varying state constraints and actuator faults. In contrast with the state-of-the-art control methodologies, the distinguishing features of this study lie in that: (a) high-order asymmetric time-varying tan-type barrier Lyapunov function (BLF) is devised such that the state variables can be convergent to the preassigned compact sets all the time provided their initial values remain therein, which not only preserves the constraints satisfaction, but warrants the validity of the adopted neural network approximator; (b) the proposed control design ensures the tracking errors converge to specified residual sets within fixed time and makes the size of the convergence regions of tracking errors adjustable a priori by means of a new BLF-based tuning function and a projection operator; (c) a variable-separable lemma is delicately embedded into the control design to extract the control terms in a “linear-like” fashion which not only overcomes the difficulty that virtual control signals appear in a non-affine manner, but also solves the problem of actuator faults. Comparative simulations results finally validate the effectiveness of the proposed scheme.

Observer‐based neural adaptive fixed‐time tracking control for multi‐input multi‐output nonlinear systems with actuator faults

“…For the investigated fault model, arbitrarily large additive fault $$$ {\bar{u}}_m\left(t,{t}_b\right) $$$ are not appropriate because of the physical restrictions on the actuator. Although the considered fault model in this work may cause some limitations on actual applications compared with a more general form of unknown time‐varying actuator failures investigated in References 53 and 54, it should be pointed out that the control scheme developed in this work can be easily extended to solve the fixed‐time adaptive FTC issue related to MIMO nonlinear plants against unknown time‐varying faults by synthesizing our results and the treatment skill for unknown fault parts in References 53 and 54.…”