Prescribed Performance Tracking Control of Nonlinear Systems Under Unknown Time-Varying Control Direction and Actuator Faults

This article investigates the prescribed performance control (PPC) problem for a class of uncertain strict-feedback systems with unknown time-varying control direction and actuator faults. A low-complexity control scheme which contains a novel control direction determination approach is proposed herein. Compared with the mainstream methods such as the Nussbaum gain and parameter estimation, the newly proposed scheme overcomes the challenge of the unknown time-varying control direction caused by actuator faults in the controller design. First, a distance function is defined, upon which a mechanism for identifying the control direction is developed. Combined with the PPC-based control law, a state feedback fault-tolerant control scheme for strict-feedback systems under unknown time-varying control coefficient is designed. Subsequently, utilizing the idea of proof by contradiction, it has been proven that under this scheme, the system tracking error can be maintained within the predefined performance criteria, while ensuring the boundedness of any closed-loop signals. Lastly, the effectiveness and merits of the proposed scheme under unknown time-varying control direction and conventional unknown control direction are verified by two sets of simulation examples, respectively.