多重受限时滞逻辑控制网络的输出跟踪

郑亚婷; 冯俊娥

doi:10.1631/FITEE.1900376

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多重受限时滞逻辑控制网络的输出跟踪

复杂系统和网络及其应用专辑 | Updated：2022-05-19

- 多重受限时滞逻辑控制网络的输出跟踪
- Output tracking of delayed logical control networks with multi-constraint
- 信息与电子工程前沿（英文） 2020年21卷第2期页码：316-323
- Affiliations：
  
  School of Mathematics, Shandong University, Jinan 250100, China
- Author bio：
  
  [ "FENG Jun-e,E-mail:fengjune@sdu.edu.cn" ]
- Funds：
  
  Project supported by the National Natural Science Foundation of China (Nos. 61773371 and 61877036) and the Natural Science Foundation of Shandong Province, China (No. ZR2019MF002)
- DOI：10.1631/FITEE.1900376
  中图分类号： O231
- 收稿：2019-07-29，
  
  修回：2019-12-19，
  
  纸质出版：2020-02
- Accepted：
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郑亚婷, 冯俊娥. 多重受限时滞逻辑控制网络的输出跟踪[J]. 信息与电子工程前沿（英文）, 2020,21(2):316-323.

ZHENG Ya-ting, FENG Jun-e. Output tracking of delayed logical control networks with multi-constraint[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(2): 316-323.
郑亚婷, 冯俊娥. 多重受限时滞逻辑控制网络的输出跟踪[J]. 信息与电子工程前沿（英文）, 2020,21(2):316-323. DOI： 10.1631/FITEE.1900376.

ZHENG Ya-ting, FENG Jun-e. Output tracking of delayed logical control networks with multi-constraint[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(2): 316-323. DOI： 10.1631/FITEE.1900376.

摘要

本文深入研究具有状态和控制受限的时滞逻辑控制网络的输出跟踪问题。与其他类型时滞相比，状态依赖型时滞数值的更新依赖当前的状态值和一个伪逻辑函数。多重受限意味着状态的取值局限在一个给定的非空集合以及控制器的设计有条件限定。采用矩阵半张量积方法将动态方程转化为代数形式，进而构造一个等价扩维系统。基于该扩维系统，输出跟踪问题被转化为集合镇定问题。利用变换的状态转移矩阵，可得到该系统实现输出跟踪的充分必要条件，通过数学软件容易验证此条件。此外，设计了状态反馈控制器使时滞逻辑控制网络的输出能跟踪参考信号。最后，通过一个例子验证本文的理论结果。

Abstract

In this study

the output tracking of delayed logical control networks (DLCNs) with state and control constraints is further investigated. Compared with other delays

state-dependent delay updates its value depending on the current state values and a pseudo-logical function. Multiple constraints mean that state values are constrained in a nonempty set and the design of the controller is conditioned. Using the semi-tensor product of matrices

dynamical equations of DLCNs are converted into an algebraic description

and an equivalent augmented system is constructed. Based on the augmented system

the output tracking problem is transformed into a set stabilization problem. A deformation of the state transition matrix is computed

and a necessary and sufficient condition is derived for the output tracking of a DLCN with multi-constraint. This condition is easily verified by mathematical software. In addition

the admissible state-feedback controller is designed to enable the outputs of the DLCN to track the reference signal. Finally

theoretical results are illustrated by an example.

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references

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