Approximation-Free Prescribed Performance Fault-Tolerant Control of Nonlinear Systems: Considering Deferred Actuator Switching

This paper addresses the prescribed performance control (PPC) problem of nonlinear systems with unknown control direction. By virtue of composite error transformation and Nussbaum gain identification, a prescribed performance controller free of approximation tool, known initial condition and control direction is proposed. We then extend it to the setting where deferred actuator switching is utilized together with error monitoring to eliminate the effect of actuator fault on PPC. By adding an input auxiliary system, the controller is improved to be capable of tolerating the switching delay of actuator, at the price of temporary performance relaxation rather than the system instability. Using proof of contradiction, it is proved that all closed-loop signals remain globally bounded in the Lyapunov sense. Two simulation examples are given to verify the superiority of the proposed approach over the existing ones. Note to Practitioners—This paper is motivated by designing an algorithm that comprises dynamic redundancy strategy to exclude the impact of actuator faults while achieving the prescribed control performance. The existing methods usually rely on the intelligent approximation, known initial condition and control direction, and require the controller redesign when the backup actuator defers the switching. Due to this consideration, we use the full-error composite transformation and Nussbaum function to derive the PPC mechanism, making the controller not only approximation-free but also applicable to any error initialization and control direction. Moreover, the input auxiliary signal is introduced such that both fault-free PPC and delays-involved redundancy PPC can be uniformly achieved by a set of control framework, which leads to low computation burden and eases the parameter tuning.