| 朱龙飞,陆超伦,李永强.基于负定不变集的吸引域估计和动态输出反馈镇定[J].高技术通讯(中文),2026,36(2):191~202 |
| 基于负定不变集的吸引域估计和动态输出反馈镇定 |
| Negative-definite invariant set approach for dynamic output feedback stabilization with domain of attraction estimation |
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| DOI：10. 3772 / j. issn. 1002 - 0470. 2026. 02. 008 |
| 中文关键词: 输出反馈； 一般非线性系统； 负定不变集； 吸引域； 区间分析 |
| 英文关键词: output feedback, general nonlinear system, negative-definite invariant set, domain of attraction, interval analysis |
| 基金项目: |
| 作者 | 单位 | | 朱龙飞 | （浙江工业大学信息工程学院杭州 310023） | | 陆超伦 | | | 李永强 | |
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| 摘要点击次数: 129 |
| 全文下载次数: 104 |
| 中文摘要: |
| 针对于一般非线性离散时间系统，提出了一种动态输出反馈控制器的设计方法。首先给出了闭环吸引域(domain of attraction, DOA)估计和动态输出反馈镇定的充分条件。对于系统状态和控制器状态的给定李雅普诺夫函数，提出了输出反馈控制下的负定不变集，该负定不变集可以被视为非结构化的动态输出反馈控制器集合，且该负定不变集在状态空间中的投影可以被视为闭环DOA的估计。基于负定不变集，控制器的设计问题就转换为欧氐空间中的一组集合近似问题。使用数值集合近似方法，处理强非线性就不再是瓶颈。其次，基于区间分析提出了一种估计负定不变集的方法，来找到所需精度的集合的内部近似。 |
| 英文摘要: |
| A design method for a dynamic output feedback controller is proposed for general nonlinear discrete-time systems. Firstly, sufficient conditions for the dynamic output feedback stabilization with an estimated domain of attraction (DOA) are provided. For a given Lyapunov function of system and controller states, a negative definite invariant set under output feedback control is introduced, which can be considered as an unstructured collection of dynamic output feedback controllers. The negative definite invariant set, projected onto the state space, serves as an estimate of the closed-loop DOA. The design problem for the controller is then transformed into a set approximation problem in Euclidean space based on the negative definite invariant set. The bottleneck of dealing with strong nonlinearity is alleviated through the use of numerical set approximation methods. Secondly, a method for estimating the negative definite invariant set is proposed based on interval analysis, aiming to find an internal approximation of the desired accuracy for the set. |
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