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 nonlinear systems subject to full-state constraints and actuator faults. In contrast with the stateof-the-art results, the distinguishing feature of our control design consists in proposing a novel high-order tantype barrier Lyapunov function (BLF) which ensures state variables to be some asymmetric time-varying compact sets under tan-type constraints and expands the application range of tan-type BLF (i.e., from low-order to high-order, from symmetric time-invariant to asymmetric time-varying). Apart from this, 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. 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 e ectiveness of the proposed scheme.