饱和开关非线性系统的非脆弱可靠保证成本控制和 L2 增益分析

Wenxiang Chen, Xinquan Zhang
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摘要

对于非线性连续时间饱和开关系统,本文研究了系统的非脆弱可靠保证成本控制问题。由于控制器扰动、执行器饱和和执行器失效同时发生,在设计代价函数时,本文在代价函数中同时考虑了控制器扰动、执行器饱和和执行器失效三种影响系统性能的情况,这在现有文献中还没有研究过。对于非线性开关系统,我们推导了一些充分条件,以同时满足非脆弱可靠保证成本控制的稳定和性能指标。为了确保非线性开关系统的指数稳定并最小化成本函数的上界,我们利用最小停留时间法设计了开关规律和非脆弱可靠保证成本状态反馈控制器。此外,通过求解线性矩阵不等式约束的优化问题,确定了成本函数的最小上界和系统性能。文章最后,我们给出了一个数值示例来验证所提方法的有效性。
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Non‐fragile reliable guaranteed cost control and L2‐gain analysis for saturated switched nonlinear systems
For the nonlinear continuous‐time saturated switched system, this article investigates the problem of non‐fragile reliable guaranteed cost control of the system. Due to the simultaneous occurrence of controller perturbation, actuator saturation and actuator failure, when designing the cost function, this article considers three scenarios affecting the system performance, controller perturbation, actuator saturation and actuator failure, simultaneously in the cost function, which has not been investigated in the existing literature. For nonlinear switched systems, we derive some sufficient conditions to satisfy simultaneously the stabilization of non‐fragile reliable guaranteed cost control and the performance index. In order to ensure the exponential stabilization of the nonlinear switched systems and minimize the upper bound of cost function, a switching law and the non‐fragile reliable guaranteed cost state feedback controllers are designed by using the minimum dwell‐time method. Furthermore, by solving optimization problems with linear matrix inequality constraints, the minimum upper bound of the cost function and the performance of the system are determined. At the end of the article, we give a numerical example to verify the effectiveness of the proposed approach.
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