L2$$ {L}_2 $$‐gain analysis and fault‐tolerant control for nonlinear discrete‐time switched systems with time‐varying delay and actuator saturation

Hu Guo, Huiju Li, Xinquan Zhang
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Abstract

The ‐gain analysis and fault‐tolerant control of a class of uncertain nonlinear discrete‐time switched systems with time‐varying delay and actuator saturation are studied by using the multiple Lyapunov functions method. The fault‐tolerant state feedback controllers and the switching law are designed such that the closed‐loop system with actuator failures satisfies the disturbance attenuation performance indicator. The problem of estimating the capacity of admissible disturbance is transformed into a constrained optimization problem to ensure that the state trajectory of the closed‐loop system is bounded under the action of external disturbances. The upper bound of restricted ‐gain is estimated by solving constrained optimization problems. Then, when the fault‐tolerant controller can be regard as the design variable, the optimization problems above are adjusted for solving control synthesis problems. Finally, the numerical example is given to verify the effectiveness of the design method.
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具有时变延迟和致动器饱和的非线性离散时间开关系统的 L2$$ {L}_2 $$ 增益分析和容错控制
利用多重 Lyapunov 函数法研究了一类具有时变延迟和执行器饱和的不确定非线性离散时间开关系统的增益分析和容错控制。设计了容错状态反馈控制器和开关规律,使执行器失效的闭环系统满足扰动衰减性能指标。将估计可接受干扰能力的问题转化为约束优化问题,以确保闭环系统的状态轨迹在外部干扰作用下是有界的。通过求解约束优化问题来估计受限增益的上限。然后,当容错控制器可视为设计变量时,对上述优化问题进行调整,以求解控制合成问题。最后,给出了数值实例来验证设计方法的有效性。
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