| 引用本文: | 徐萌,张成科,曹铭.转移概率一般有界的Markov跳变系统有限时间保成本控制[J].控制理论与应用,2025,42(4):749~756.[点击复制] |
| XUmeng,XUmeng,Caoming.Finite-time guaranteed cost control for stochastic Markov jump system with genernally bounded transition probabilities[J].Control Theory & Applications,2025,42(4):749~756.[点击复制] |
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| 转移概率一般有界的Markov跳变系统有限时间保成本控制 |
| Finite-time guaranteed cost control for stochastic Markov jump system with genernally bounded transition probabilities |
| 摘要点击 5 全文点击 1 投稿时间：2023-10-28 修订日期：2025-03-15 |
| 查看全文 查看/发表评论 下载PDF阅读器 |
| DOI编号 10.7641/CTA.2024.30704 |
| 2025,42(4):749-756 |
| 中文关键词 Markov跳变系统 转移概率一般有界 有限时间随机稳定 保成本控制 |
| 英文关键词 Markovjumpsystem generally bounded transition probabilities finite-time stochastic stability guaranteed cost control |
| 基金项目 国家自然科学基金项目(7157053),国家社科基金项目(21FGYB205),广东基础及应用基础研究基金项目(2023A1515012335)资助. |
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| 中文摘要 |
| 针对系统信息不完全,本文研究了转移概率一般有界的随机Markov跳变系统有限时间控制问题.一般有界
涵盖了部分未知、有界不确定和一般不确定3种不完全转移概率的情况.首先,研究该系统有限时间随机稳定问题,
引入自由连接权矩阵分离未知转移概率信息,给出开环系统有限时间稳定的充分性判据;其次,借助Lyapunov方法
和完全平方技术,得到了实现系统有限时间保成本控制的充分条件,给出了控制增益的设计方式以及性能指标的精
确上界;最后,以太阳能锅炉控制系统为实例进行数值仿真,说明本研究结果的有效性和实用性. |
| 英文摘要 |
| Aiming at the issue of incomplete system information, this paper investigates the finite-time guaranteed cost
control theory for stochastic Markov jump system with generally bounded transition probabilities, which is composed of
three scenarios of incomplete transition probabilities: partially unknown, bounded uncertainties, and general uncertainties.
Firstly, the finite-time stochastic stability problem is explored. By introducing a free connection weight matrix to decouple
the unknown transition probability information, a sufficient criterion for the finite-time stability of the open-loop system is
derived. Secondly, with the help of Lyapunov method and complete square technique, the sufficient conditions for realizing
the finite-time guaranteed cost control of the system are obtained, and the design method of control gain and the exact upper
bound of performance index are given. Finally, numerical simulations based on a solar boiler control system are conducted
to demonstrate the validity and practicality of the research findings. |
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