随机测量噪声下Lipschitz非线性系统基于事件触发脉冲观测器镇定

doi:10.12141/j.issn.1000-565X.230012

华南理工大学学报(自然科学版) ›› 2023, Vol. 51 ›› Issue (11): 35-43.doi: 10.12141/j.issn.1000-565X.230012

所属专题： 2023年电子、通信与自动控制

• 电子、通信与自动控制 • 上一篇下一篇

随机测量噪声下Lipschitz非线性系统基于事件触发脉冲观测器镇定

罗世贤¹ 陈鑫¹ 黄敢基²

^1.广西大学电气工程学院，广西南宁 530004
^2.广西大学数学与信息科学学院/广西应用数学中心，广西南宁 530004

收稿日期:2023-01-10 出版日期:2023-11-25 发布日期:2023-04-24
通信作者: 黄敢基（1972-），男，博士，教授，主要从事混杂系统控制理论研究。 E-mail:ganjih@163.com
作者简介:罗世贤（1989-），男，助理教授，硕士生导师，主要从事随机混杂系统控制理论研究。E-mail: shixianluo@126. com
基金资助:
国家自然科学基金资助项目(62003104);广西自然科学基金资助项目(2022GXNSFBA035649);广西大学自然科学与技术创新发展倍增计划项目(2023BZRC018);广西科技基地和人才专项(桂科AD23026217);广西大学学科交叉科研项目(2022JCC019)

Event-Triggered Impulsive Observer-Based Stabilization for Lipschitz Nonlinear Systems with Discrete-Time Stochastic Measurement Noises

LUO Shixian¹ CHEN Xin¹ HUANG Ganji²

^1.School of Electrical Engineering，Guangxi University，Nanning 530004，Guangxi，China
^2.School of Mathematics and Information Science/ Center for Applied Mathematics of Guangxi，Guangxi University，Nanning 530004，Guangxi，China

Received:2023-01-10 Online:2023-11-25 Published:2023-04-24
Contact: 黄敢基（1972-），男，博士，教授，主要从事混杂系统控制理论研究。 E-mail:ganjih@163.com
About author:罗世贤（1989-），男，助理教授，硕士生导师，主要从事随机混杂系统控制理论研究。E-mail:shixianluo@126. com
Supported by:
the National Natural Science Foundation of China(62003104);the Guangxi Natural Science Foundation(2022GXNSFBA035649)

摘要/Abstract

摘要：

为了提高计算或通信资源的利用率，减少能源的消耗，文中在经典的连续时间动态输出反馈控制的基础上，针对一类非周期采样和随机测量噪声下的Lipschitz非线性系统，提出了一种基于事件触发脉冲观测器的输出反馈控制方法。首先，通过设计只依赖于系统离散测量输出与辅助变量的事件触发机制，构建了一种新型事件触发脉冲观测器，而后通过构造由原系统与观测误差系统组成的增广系统，发展拟周期离散化Lyapunov函数方法，建立了增广闭环系统均方意义下最终有界的稳定性判据，该判据揭示了采样周期、噪声强度和事件触发参数对系统性能的影响机理；然后，通过联合设计方法，将求解原系统的输出反馈控制器与观测误差系统的观测器增益问题转换为求解一组基于增广系统的线性矩阵不等式（LMI）可行解问题，以解决随机测量噪声下无法分离设计控制增益与观测增益的难题；最后，在Matlab平台上，以连杆机械臂系统为例分析所提控制方法的性能。实验结果表明，文中所提方法能够有效地减少系统状态的传输次数，降低通信/计算资源的消耗，解决了存在随机测量噪声的非线性系统镇定问题，从而验证了所提方法的有效性。

关键词: 事件触发控制, 脉冲观测器, 反馈控制, 随机噪声

Abstract:

In order to improve the utilization of computing or communication resources and reduce energy consumption, the study proposed the event-triggered impulsive observer-based output feedback control method for a class of nonlinear systems with aperiodic sampling and stochastic measurement noises. Firstly, by introducing an event-triggering mechanism that only depends on the discrete-time measurement output and an auxiliary variable, it designed a novel event-triggered impulsive observer. Then by constructing an augmented system composed of the original system and the observer error system and developing the quasi-periodic discretized Lyapunov function method, it established an ultimate bounded stability criterion in the mean square sense of the augmented closed-loop systems. The criterion reveals the influence mechanism of the sampling period, noise intensity, and event trigger parameters on system performance. Next, combined with the joint design approach, the output feedback controller synthesis problem was transformed into solving a set of LMIs based on the augmented system, thus solving the difficult problem that the state feedback gain and the observer gain cannot be separated in the presents of the stochastic measurement noise. Finally, on the Matlab platform, the performance of the proposed control method was analyzed via a connecting rod robotic arm. The experimental results demonstrate that the proposed method is effective in reducing the number of transmissions and conserving communication/computing resources. Furthermore, it successfully addresses the stabilization problems of nonlinear systems with stochastic measurement noise, thus confirming the effectiveness of the proposed approach.

Key words: event-triggered control, impulsive observer, feedback control, stochastic noise

中图分类号:

TP273

罗世贤, 陈鑫, 黄敢基. 随机测量噪声下Lipschitz非线性系统基于事件触发脉冲观测器镇定[J]. 华南理工大学学报(自然科学版), 2023, 51(11): 35-43.

LUO Shixian, CHEN Xin, HUANG Ganji. Event-Triggered Impulsive Observer-Based Stabilization for Lipschitz Nonlinear Systems with Discrete-Time Stochastic Measurement Noises[J]. Journal of South China University of Technology(Natural Science Edition), 2023, 51(11): 35-43.

图/表 3

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N	δ_max/s			N	δ_max/s
1	0.19			10	0.46
5	0.39			20	0.52

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随机测量噪声下Lipschitz非线性系统基于事件触发脉冲观测器镇定

Event-Triggered Impulsive Observer-Based Stabilization for Lipschitz Nonlinear Systems with Discrete-Time Stochastic Measurement Noises

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