This paper investigates the performance-guaranteed adaptive self-healing control for wastewater treatment processes (WWTPs), in which the non-ideal actuator, i.e., the actuator suffering from faults and constraints is considered. Firstly, an error conversion dynamic model based on a new prespecified-time performance function is presented to guarantee that the tracking error is quickly maintained in the user-defined area regardless of the occurrence of actuator faults and constraints. Secondly, a novel smooth approximation function is constructed to imitate the non-smooth characteristics of actuator constraints. Thirdly, the unknown bounds of non-ideal actuator parameters are estimated online in place of parameters themselves. Meanwhile, the lumped disturbances induced by the external disturbance and the fuzzy approximation error are suppressed via $H_{\infty }$ control theory. In addition, the stability analysis is carried out by the Lyapunov stability criterion to guarantee that all closed-loop system signals are bounded. Finally, comparative simulation results demonstrate that the proposed method has the superiorities in terms of preferable dynamic tracking performance with fast transient convergence, strong robustness and performance recovery under non-ideal actuator.

本文研究了废水处理过程（WWTPs）的性能保证自适应自愈控制，其中考虑了非理想执行器，即存在故障和约束的执行器。首先，提出了一种基于新的预定时间性能函数的误差转换动态模型，以保证跟踪误差在用户定义的区域内快速保持，而不受执行器故障和约束的发生。其次，构造了一种新颖的平滑逼近函数来模拟执行器约束的非平滑特性。第三，在线估计非理想执行器参数的未知范围以代替参数本身。同时，外部干扰引起的集总干扰和模糊逼近误差通过以下方法得到抑制：$H_{\infty }$控制理论。此外，通过李雅普诺夫稳定性准则进行稳定性分析，以保证所有闭环系统信号都是有界的。最后，对比仿真结果表明，该方法具有较好的动态跟踪性能、瞬态收敛速度快、鲁棒性强、在非理想执行器下性能恢复等优点。