# Performance-Constraint Fault Tolerant Control to Aircraft in Presence of Actuator Deviation
## 1 Introduction  
The control-stability of aircraft depends on actuator operating condition, its stable output is the prerequisite to achieve reliable flight, high speed flight vehicles are particularly sensitive to actuator performance. Accuracy of electro-mechanical or hydraulic actuators is easily deteriorated in complex flight environment such as electromagnetic interference, low temperature or leakage. In this situation, a fault-tolerant control is expected to accommodate actuator deviation within a certain range [1]. Research works of dealing with actuator failure are presented in a variety of ways, for instance, the model prediction control [2], multi-variable integral terminal sliding mode control [3], incremental nonlinear FTC [4], and intelligent methods [5, 6]. Estimation and compensation to system failures are the key thoughts in active FTC strategy. [PERSON] [7] developed an intelligent fault diagnosis approach and corresponding disturbance compensation control for hypersonic vehicles. One primary problem is that a high convergence speed of fault estimation module will amplify the noisy signal, further, [PERSON]. [8] proposed an output-feedback fault-tolerance method for the non-affine actuator faults, thus input nonlinearity of system is considered. [PERSON] [9] reconstructed the unmatched actuator faults in sliding-mode control scheme, which can keep a rapid convergence speed to some certain faults. An online dynamics reconstruction scheme is established for more broader actuator failure based on adaptive observer [10]. [PERSON] [11] developed a quasi linear-parameter-varying observer to achieve fault detection and isolation for the quad-rotor vehicles. Other studies such as the faults estimators [12, 13] and fuzzy nonlinear observer [14] are also very effective. The main characteristic of estimation and compensation frame lies in an additional system module,and its stability depends on carefully parameters selection. Therefore, direct FTC methods have also been paid attention. [PERSON] [15] designed a robust FTC framework by introducing back-stepping control technique in unmanned helicopters. Linear parameter varying (LPV) methodology [16] showed the robust performance to aileron and rudder loss-of-efficiency faults, based on it, a virtual actuators was reconfigured to mitigate fault effects [17]. Generally, adaptive control schemes are often designed together with a recurrent neural networks [18], linear quadratic regulator [19], dynamic control allocation [20] in active fault-tolerant control. It is worth noting that there needs a trade-off between robustness of close-loop system and convergence speed in direct FTC schemes. Obviously, the rapid stabilizing ability is one of the goals even failure occurs, especially for the inner-loop attitude dynamics in aircraft, thereby finite-time-convergence theory on the autonomous systems is often introduced into the attitude controller [21; 22]. Compared with the exponential convergence methods, it has faster convergence rate while usually along with a large instantaneous output. Meanwhile, Flight manage system needs to limit the kinematic speed of air vehicle once the capability fade of actuators to ensure states are always in the safe boundary to a flawed system, it is deemed to be a regulation problem of nonlinear system together with state restriction. The barrier-Lyapunov function is an effective analysis tool [23; 24; 25] to this kind of issue, it has applied to different rigid body objects including the quadrotor [26], underwater vehicle [27], and hypersonic aerocraft [28]. The main contribution in this paper lies in unifying the practical FTC approach and barrier-Lyapunov tool into a new control paradigm, then establishing a finite-time-convergence fault-tolerant (FTC-FT) controller, and it has an adaptive mechanism to balance the robustness and dynamic capability for a flawed system.