引用本文:廖福成,吴莹雪.线性连续时间时滞系统的有限时间有界跟踪控制[J].控制与决策,2019,34(10):2095-2104
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线性连续时间时滞系统的有限时间有界跟踪控制
廖福成,吴莹雪
(北京科技大学数理学院,北京100083)
摘要:
研究一类线性连续时间时滞系统的有限时间有界跟踪控制问题.首先,采用预见控制理论中求导的方法构造带有时滞的误差系统,把误差信号的信息包含在误差系统的状态向量中,再将其作为误差系统的输出向量;其次,通过为误差系统设计一个有记忆的状态反馈控制器,把问题转化为研究带有时滞的误差系统的闭环系统输入-输出有限时间稳定问题;再次,借鉴输入-输出有限时间稳定的研究方法和线性矩阵不等式的方法, 通过构造Lyapunov-Krasovskii函数,给出由一组线性矩阵不等式表征的控制器增益矩阵的设计方法,由此得到原系统的一个有限时间有界跟踪控制器;最后,通过一个数值实例验证所设计的控制器的有效性和优越性.
关键词:  连续时间时滞系统  误差系统  预见控制  输入-输出有限时间稳定  跟踪控制  线性矩阵不等式
DOI:10.13195/j.kzyjc.2018.0190
分类号:TP273
基金项目:科技部重点研发计划项目(2017YFF0207400).
Finite-time bounded tracking control for linear continuous systems with time-delay
LIAO Fu-cheng,WU Ying-xue
(School of Mathematics and Physics,University of Science and Technology Beijing,Beijing100083,China)
Abstract:
A finite-time bounded tracking control problem is investigated for a class of linear continuous systems with time-delay. Firstly, by applying a derivation method in the theory of preview control to constructing the error system with time-delay, the error signal is included in the state vector of it and then considered as the output vector. Then, the problem is transformed into an input-output finite-time stability problem of the closed-loop system of the error system, by designing a memory state feedback controller for the error system. Forthermore, based on the research methods of input-output finite-time stability and linear matrix inequation methods, the controller gains formulated in forms of linear matrix inequalities are provided by constructing a Lyapunov-Krasovskii functional. From this, a finite-time bounded tracking controller of the original system is obtained. Finally, a numerical example is given to illustrate the effectiveness and superiority of the proposed controller.
Key words:  continuous systems with time-delay  error system  preview control  input-output finite-time stability  tracking control  linear matrix inequality

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