基于一种分段泛函的马尔可夫跳变系统的采样控制

王庆; 张益

doi:10.13442/j.gnss.1008-9268.2020.05.014

基于一种分段泛函的马尔可夫跳变系统的采样控制

doi: 10.13442/j.gnss.1008-9268.2020.05.014

王庆,
张益

东南大学仪器科学与工程学院,江苏南京 210096

详细信息

作者简介:
王庆 (1962—),男,博士,教授,研究方向为北斗高精度位置监测.

通讯作者:
王庆 E-mail:woaoqq477@163.com

计量
- 文章访问数: 298
- HTML全文浏览量: 56
- PDF下载量: 12
- 被引次数: 0
出版历程
- 刊出日期: 2021-02-24

Sampled-data control of Markov jump system via a fragmentation functional

WANG Qing,
ZHANG Yi

College of Instrument Science and Engineering,Southeast University,Nanjing 210096,China

摘要

摘要: 马尔可夫跳变系统（MJSs）是实际应用中一种极其重要的混合随机系统,本文研究了MJSs的采样控制问题．根据一种连续的MJSs模型和Lyapunov-Krasovskii稳定性定理,通过引入两个可调参数,首先把整个采样区间分段成了四个部分,基于四个采样区间提出了相应的两个状态空间表达式,利用这两个状态空间表达式,构建了一种能够充分利用四个分段区间状态信息的新颖Lyapunov-Krasovskii泛函,再利用积分不等式方法去估计泛函导数,从而获得采样控制MJSs的全新稳定性判据．最后,给出了一个非线性质量弹簧阻尼器系统例子和一个实际的船舶定位系统例子,经过建立仿真,所得到的采样区间最大值远远大于相似文献的结果,表明了本文方法的优越性．
- 马尔可夫跳变系统 /
- 采样控制 /
- 分段泛函
Abstract: Markovian jump systems is a most important mixed stochastic system in practice application,the sampled-data control problem of Markov jump system is studied in this paper.According to a continuous Markov jump system model and Lyapunov-Krasovskii stability theorem,the whole sampling interval is divided into four parts by introducing two adjustable parameters.Based on the four sampling intervals,two corresponding expressions of state space are proposed.Novel Lyapunov-Krasovskii functional which can fally use the status information of four frogmentation interual is built.then,using the integral inequality methods to estimate functional derivative,a new sampled-data control Markov jump system stability criterion is obtained.Finally,an example of a nonlinear mass spring damper system and an actual ship positioning system are given.After the establishment of simulation,the maximum sampling interval obtained is much larger than the results of similar literatures,indicating the superiority of the method.
- Markov jump system /
- sampled-data control /
- fragmentation functional

HTML全文

参考文献(20)

[1]	LI H,WANG Y Y,YAO D Y,et al.A sliding mode approach to stabilization of nonlinear Markovian jump singularly perturbed systems［J］.Automatica,2018（97）:404-413.DOI: 10.1007／978-3-211-73017-1.
[2]	高学泽,魏文军.马尔可夫参数自适应IMM算法在列车定位中的应用［J］.传感器与微系统,2019,38(1):155-157,160.
[3]	吴庆祥,DAVID B.可移动机器人的马尔可夫自定位算法研究［J］.自动化学报,2003,29(1):154-160.
[4]	唐龙,张小红,吕翠仙,等.精密单点定位估计GPS卫星的P1-C1码偏差及稳定性分析［J］.全球定位系统,2011,36(2):1-5.
[5]	罗峰.CORS基准站的稳定性分析与研究［J］.全球定位系统,2014,39(1):42-45,55.
[6]	KWON N K,PARK I S,PARK P G.H∞control for singular markovian jump systems with incomplete knowledge of transition probabilities［J］.Applied mathematics and computation,2017（295）:126-135.DOI: 10.1016／j.amc.2016.09.004.
[7]	KWON N K,PARK I S,PARK P G,et al.Dynamic output-feedback control for singular markovian jump system:LMI approach［J］.IEEE transactions on automatic control,2017,62(10):5396-5400.DOI: 10.1109／TAC.2017.2691311.
[8]	WU Z G,SHI P,SU H,et al.Sampled-data exponential synchronization of complex dynamical networks with time-varying coupling delay［J］.IEEE transactions on neural networks and learning systems,2013,24(8):1177-1187.DOI: 10.1109／TNNLS.2013.2253122.
[9]	ZHAO D W,DING F G,ZHOU L,et al.Robust H∞control of neutral system with time-delay for dynamic positioning ships［J］.Mathematical problems in engineering,2015.DOI: 10.1155／2014／976925.
[10]	YANG S,ZHENG M.H∞fault-tolerant control for dynamic positioning ships based on sampled-data［J］.Journal of control engineering and applied informatics,2018,20(4):32-39.
[11]	ZHENG M J,ZHOU Y J,YANG S H,et al.Robust H∞control of neutral system for sampled-data dynamic positioning ships［J］.IMA journal of mathematical control and information,2019,36(4):1325-1345.DOI: 10.1093／imamci／dny029.
[12]	WANG Y Y,XIA Y Q,ZHOU P F.Fuzzy-model-based sampled-data control of chaotic systems:a fuzzy time-dependent lyapunov—krasovskii functional approach［J］.IEEE transactions on fuzzy systems,2017,25(6):1672-1684.DOI: 10.1109／TFUZZ.2016.2617378.
[13]	XU S D,SUN G H,LI Z,et al.Finite-time robust fuzzy control for non-linear Markov jump systems under aperiodic sampling and actuator constraints［J］.IET control theory ＆ applications,2017,11(15):2419-2431.DOI: 10.1049／iet-cta.2016.1609.
[14]	MA W W,JIA X C,YANG F W,et al.An impulsive-switched-system approach to aperiodic sampled-data systems with time-delay control［J］.International journal of robust and nonlinear control,2018,28(4):2484-2494.DOI: 10.1002／rnc.4030.
[15]	SEURET A.A novel stability analysis of linear systems under asynchronous samplings［J］.Automatica,2012, 48(1):177-182.DOI: 10.1016／j.automatica.2011.09.033.
[16]	ZENG H B,TEO K L,HE Y.A new looped-functional for stability analysis of sampled-data systems［J］.Automatica,2017（82）:328-331.DOI: 10.1016／j.automatica.2017.04.051.
[17]	HU L S,SHI P,FRANK P M.Robust sampled-data control for Markovian jump linear systems［J］.Automatica,2006,42(11):2025-2030.DOI: 10.1016／j.automatica.2006.05.029.
[18]	SHEN H,PARK J H,ZHANG L X,et al.Robust extended dissipative control for sampled-data Markov jump systems［J］.International journal of control,2014,87(8):1549-1564.DOI: 10.1080／00207179.2013.878478.
[19]	PARK J M,PARK P G.Sampled-data control for continuous-time Markovian jump linear systems via a fragmented-delay state and its state-space model［J］.Journal of the franklin institute,2019,356(10):5073-5086.DOI: 10.1016／j.jfranklin.2019.02.033.
[20]	ZHANG X M,HAN Q L,ZENG Z G.Hierarchical type stability criteria for delayed neural networks via canonical Bessel-Legendre inequalities［J］.IEEE transactions on cybernetics,2018,48(5):1660-1671.DOI: 10.1109／TCYB.2017.2776283.