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.