Global Singularity-Free Prescribed Performance Control for Faulty Nonlinear Systems via Parameterized Nonmonotonic Constraints

In this paper, we investigate potential singularity issues in prescribed performance control induced by actuator faults and propose a global nonmonotonic prescribed performance scheme for strict-feedback nonlinear systems. This scheme allows for parameterized relaxation of constraint boundaries in the presence of actuator faults. Unlike existing prescribed performance control schemes that rely on redesigning nonmonotonic rate functions to modify boundary relaxation properties, the proposed method introduces a novel adjustment module into the prescribed performance function, enabling the parametric design of nonmonotonic boundaries. Moreover, the proposed method simultaneously addresses the removal of the initial feasibility condition and the imposition of asymmetric constraints by introducing a global asymmetric design with an error correction module. This module enables flexible conversion from asymmetric to symmetric boundaries at a predetermined time instant, thereby reducing transient overshoot while maintaining steady-state tracking precision. Simulation results validate the effectiveness and superiority of the proposed scheme.