Stabilization of Continuous-Time Probabilistic Logical Networks Under Sampling Dwell Time Constraints

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization Pub Date : 2024-03-19 DOI:10.1137/23m1566388

Lin Lin, James Lam, Min Meng, Xiaochen Xie, Panshuo Li, Daotong Zhang, Peng Shi

{"title":"Stabilization of Continuous-Time Probabilistic Logical Networks Under Sampling Dwell Time Constraints","authors":"Lin Lin, James Lam, Min Meng, Xiaochen Xie, Panshuo Li, Daotong Zhang, Peng Shi","doi":"10.1137/23m1566388","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 2, Page 1006-1033, April 2024. <br/>Abstract.This paper investigates the sampled-data stabilization of continuous-time probabilistic logical control networks (CT-PLCNs). CT-PLCNs can provide quantitative and accurate descriptions for the transient kinetics in comparing discrete-time probabilistic logical control networks (DT-PLCNs). First, CT-PLCNs are transformed into switched continuous-time probabilistic logical networks by regarding the control input as a switching signal. In this setup, CT-PLCNs can be classified into two types: one with stable modes and the other with only unstable modes. Then the concept of average [math]-sample dwell time is proposed to describe the scenario, where the dwell time of each mode is an integral multiple of the sampling period [math]. Based on this, the stabilization conditions for CT-PLCNs are established by restricting the sampling dwell time of controller modes. Furthermore, a copositive Lyapunov function is constructed for the case with stable modes and is discretized for the case without stable modes, providing a new framework for studying the stabilization of CT-PLCNs. Finally, a chemical model generated by GINsim is provided to demonstrate the feasibility of the obtained theoretical results. Overall, this paper provides new insights into the stabilization of CT-PLCNs and presents practical applications for chemical models.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Control and Optimization","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1566388","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}

引用次数: 0

Abstract

SIAM Journal on Control and Optimization, Volume 62, Issue 2, Page 1006-1033, April 2024.
Abstract.This paper investigates the sampled-data stabilization of continuous-time probabilistic logical control networks (CT-PLCNs). CT-PLCNs can provide quantitative and accurate descriptions for the transient kinetics in comparing discrete-time probabilistic logical control networks (DT-PLCNs). First, CT-PLCNs are transformed into switched continuous-time probabilistic logical networks by regarding the control input as a switching signal. In this setup, CT-PLCNs can be classified into two types: one with stable modes and the other with only unstable modes. Then the concept of average [math]-sample dwell time is proposed to describe the scenario, where the dwell time of each mode is an integral multiple of the sampling period [math]. Based on this, the stabilization conditions for CT-PLCNs are established by restricting the sampling dwell time of controller modes. Furthermore, a copositive Lyapunov function is constructed for the case with stable modes and is discretized for the case without stable modes, providing a new framework for studying the stabilization of CT-PLCNs. Finally, a chemical model generated by GINsim is provided to demonstrate the feasibility of the obtained theoretical results. Overall, this paper provides new insights into the stabilization of CT-PLCNs and presents practical applications for chemical models.

查看原文本刊更多论文

采样停留时间限制下连续时间概率逻辑网络的稳定问题

SIAM 控制与优化期刊》第 62 卷第 2 期第 1006-1033 页，2024 年 4 月。摘要：本文研究了连续时间概率逻辑控制网络（CT-PLCNs）的采样数据稳定问题。与离散时间概率逻辑控制网络（DT-PLCNs）相比，CT-PLCNs 可以对瞬态动力学进行定量和精确的描述。首先，将控制输入视为开关信号，将 CT-PLCN 转化为开关式连续时间概率逻辑网络。在这种设置下，CT-PLCN 可分为两类：一类具有稳定模式，另一类仅具有不稳定模式。然后提出平均[math]-采样停留时间的概念来描述这种情况，其中每个模式的停留时间是采样周期的整数倍[math]。在此基础上，通过限制控制器模式的采样停留时间，建立了 CT-PLCN 的稳定条件。此外，还为有稳定模式的情况构建了共正 Lyapunov 函数，并对无稳定模式的情况进行了离散化处理，从而为研究 CT-PLCN 的稳定问题提供了新的框架。最后，本文提供了一个由 GINsim 生成的化学模型，以证明所获理论结果的可行性。总之，本文为 CT-PLCN 的稳定化提供了新的见解，并介绍了化学模型的实际应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

SIAM Journal on Control and Optimization 数学-应用数学

CiteScore

4.00

自引率

4.50%

发文量

143

审稿时长

12 months

期刊介绍： SIAM Journal on Control and Optimization (SICON) publishes original research articles on the mathematics and applications of control theory and certain parts of optimization theory. Papers considered for publication must be significant at both the mathematical level and the level of applications or potential applications. Papers containing mostly routine mathematics or those with no discernible connection to control and systems theory or optimization will not be considered for publication. From time to time, the journal will also publish authoritative surveys of important subject areas in control theory and optimization whose level of maturity permits a clear and unified exposition. The broad areas mentioned above are intended to encompass a wide range of mathematical techniques and scientific, engineering, economic, and industrial applications. These include stochastic and deterministic methods in control, estimation, and identification of systems; modeling and realization of complex control systems; the numerical analysis and related computational methodology of control processes and allied issues; and the development of mathematical theories and techniques that give new insights into old problems or provide the basis for further progress in control theory and optimization. Within the field of optimization, the journal focuses on the parts that are relevant to dynamic and control systems. Contributions to numerical methodology are also welcome in accordance with these aims, especially as related to large-scale problems and decomposition as well as to fundamental questions of convergence and approximation.