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33rd Chinese Control and Decision Conference (CCDC)

作者： Zuo, Huang Dai, Xisheng Zhang, Jianxiang Guangxi Univ Sci & Technol Sch Elect & Informat Engn Liuzhou 545000 Peoples R China

ISBN: (纸本)9781665440899

This paper investigates the problem of finite-time stability (FTS) and finite-time stabilization problem for a class of linear Ito-type stochastic parabolic distributed parameter systems. First, the concept of FTS and finite-time stabilization in mean square sense are proposed. Second, several sufficient conditions are given for the concerned systems to be finite-time stable by introducing a Lyapunov function and utilizing linear matrix inequalities (LMIs) technique. Moreover, the results of finite-time stabilization were also given. Finally, a numerical example is given to illustrate the effectiveness of our results.

关键词： stochastic distributed parameter systems Finite-time stability Linear matrix inequality State feedback

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Finite-Time Stability and Stabilization of Linear stochastic Parabolic distributed parameter systems

Finite-Time Stability and Stabilization of Linear Stochastic...

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第33届中国控制与决策会议

作者： Huang Zuo Xisheng Dai Jianxiang Zhang School of Electrical and Information Engineering Guangxi University of Science and Technology

This paper investigates the problem of finite-time stability(FTS) and finite-time stabilization problem for a class of linear Ito-type stochastic parabolic distributed parameter ***,the concept of FTS and finite-time stabilization in mean square sense are ***,several sufficient conditions are given for the concerned systems to be finite-time stable by introducing a Lyapunov function and utilizing linear matrix inequalities(LMIs) ***,the results of finite-time stabilization were also ***,a numerical example is given to illustrate the effectiveness of our results.

关键词： stochastic distributed parameter systems Finite-time stability Linear matrix inequality State feedback

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Controlling a class of stochastic distributed parameter systems using mobile sensor-actuator networks with missing measurements

Controlling a class of stochastic distributed parameter syst...

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Chinese Automation Congress (CAC)

作者： Zhang, Jianzhong Cui, Baotong Jiangnan Univ Sch IoT Engn Wuxi Peoples R China

ISBN: (纸本)9781538635247

This article investigates a mobile control problem for a class of stochastic distributed parameter systems with moving boundaries by using mobile sensor-actuator networks(MSANs). The network induced randomly missing measurements among the sensors are introduced for their universal existence in sensor networks. The collocated sensor-actuator networks which can travel throughout the spatial domain are assumed to be able to provide almost locally measurements and implement the related control behavior. Two strategies are obtained based on different assumptions on different modes of messaging. It is proved that the mobile control strategy of the MSANs which is obtained based on the Lyapunov's method and Ito differential formula, is greatly affected by the moving boundary. A numerical example is given to verify the effectiveness of the proposed mobile control policy.

关键词： stochastic distributed parameter systems mobile sensor-actuator networks missing measurements Lyapunov method Ito differential formula

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Mobile control for a class of stochastic distributed parameter systems with time-dependent spatial domains 36

Mobile control for a class of stochastic distributed paramet...

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第36届中国控制会议

作者： Jianzhong Zhang Baotong Cui School of Internet of Things Engineering Jiangnan University

ISBN: (纸本)9781538629185

In this article, a mobile control scheme is proposed for a class of stochastic distributed parameter systems with timedependent spatial domains with the aid of a mobile actuating device equipped with a simple output feedback controller. The almost locally distributed state information is assumed to be provided by sensors dotted about the spatial domain where the moving actuating device is able to travel throughout. Two strategies are obtained based on different assumptions on the dynamic behavior of the actuating device. It is proved that the mobile strategy of the actuating device, which is obtained based on the Lyapunov’s method and It? differential formula, is greatly affected by the time-dependent spatial domain. Simulation results show that the proposed mobile control policy is effective.

关键词： stochastic distributed parameter systems Time-dependent spatial domains Mobile control It? differential formula

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Mean-square exponential stability of stochastic Volterra systems in infinite dimensions

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Science China(Information Sciences) 2024年第10期67卷 298-314页

作者： Lin FU Shiguo PENG Feiqi DENG Quanxin ZHU School of Automation Guangdong University of Technology School of Automation Science and Engineering South China University of Technology Key Laboratory of Computing and Stochastic Mathematics(Ministry of Education) School of Mathematics and StatisticsHunan Normal University

Over the past decade, the study of stability theory in integro-differential systems has grown significantly owing to their relevance in solving physical and engineering problems, such as viscoelasticity and thermo-viscoelasticity in materials with memory properties. This paper concentrates on a class of infinite-dimensional stochastic integro-differential systems. We establish the well-posedness of the system and identify mild solutions to the system and an abstract stochastic Cauchy problem. This identification is identified by employing a semigroup approach combined with Yosida approximation. We derive sufficient conditions that ensure the mean-square exponential stability of mild solutions to the system boils down to the boundedness of a certain function and a norm estimate for the stochastic part. These conditions are implemented through the semigroup approach and the composition operator method. Illustrative examples are provided and the obtained theoretical results are validated by numerical simulations.

关键词： stochastic integro-differential equations mean-square exponential stability stochastic distributed parameter systems Hardy space composition operators

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A unified criterion for semiglobal and global finite/fixed-time stability of stochastic systems

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INTERNATIONAL JOURNAL OF systems SCIENCE 2025年

作者： Fu, Lin Peng, Shiguo Zhu, Quanxin Zhuang, Jiawei Guangdong Univ Technol Sch Automat Guangzhou 510006 Guangdong Peoples R China Hunan Normal Univ Sch Math & Stat MOE LCSM Changsha Hunan Peoples R China Guangdong Univ Finance Sch Internet Finance & Informat Engn Guangzhou Guangdong Peoples R China

In this paper, semiglobal and global finite/fixed-time stability of a class of semilinear stochastic systems in Hilbert spaces are studied. By employing the stopping time technique and applying the infinite-dimensional It & ocirc;formula, a unified Lyapunov criterion is established under which global finite-time, global fixed-time, semiglobal finite-time and semiglobal fixed-time stability can all be obtained. This fills the research gaps in the finite/fixed-time stability of stochastic distributed parameter systems and the semiglobal finite/fixed-time stability of stochastic systems. Moreover, compared to existing results on finite/fixed-time stability for stochastic systems, our Lyapunov criterion can still work well under more stringent conditions. This is done by adding a term which can reflect the stabilising effect of the diffusion term and replacing original fractional power functions with a class of piecewise continuous fractional power functions that are no longer required to be increasing. Finally, illustrative examples are given and the obtained theoretical results are verified by numerical simulations.

关键词： stochastic distributed parameter systems semiglobal finite-time stability semiglobal fixed-time stability

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Finite-dimensional observer-based boundary control fora one-dimensional stochastic heat equation

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systems & CONTROL LETTERS 2025年 197卷

作者： Shang, Yu-Shuo Wu, Ze-Hao Zhou, Hua-Cheng Cent South Univ Sch Math & Stat HNP LAMA Changsha 410075 Hunan Peoples R China Foshan Univ Sch Math Foshan 528000 Peoples R China

In this article, we investigate the finite-dimensional observer-based boundary control fora one-dimensional stochastic heat equation with nonlinear multiplicative noise and non-local sensing measurement. We adopt the modal decomposition to divide the system into two subsystems: one unstable with finite positive eigenvalues and the other essentially stable. We design the controller for the unstable subsystem by dynamic extension and demonstrate that the proposed controller actually leads to the resulting closed-loop system to be well-posed and exponentially stable, both in the mean square and almost sure senses. Finally, some numerical simulations are performed to illustrate the effectiveness of the proposed method.

关键词： stochastic distributed parameter systems Output feedback Boundary control Exponential stability

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Observer-Based Fuzzy Quantized Control for a stochastic Third-Order Parabolic PDE System

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IEEE TRANSACTIONS ON systems MAN CYBERNETICS-systems 2023年第1期53卷 485-494页

作者： Kang, Wen Wang, Xiao-Nan Guo, Bao-Zhu Beijing Inst Technol Sch Math & Stat Beijing 100081 Peoples R China Beijing Inst Technol MIIT Key Lab Math Theory & Computat Informat Secu Beijing 102488 Peoples R China Univ Sci & Technol Beijing Sch Automat & Elect Engn Beijing 100083 Peoples R China Univ Sci & Technol Beijing Shunde Grad Sch Foshan 528399 Peoples R China Acad Sinica Acad Math & Syst Sci Beijing 100190 Peoples R China

The work addresses an observer-based fuzzy quantized control for stochastic third-order parabolic partial differential equations (PDEs) using discrete point measurements. For the first time, we contribute in introducing three types of quantizer-logarithmic quantizer, uniform quantizer, and hysteresis quantizer into the controller designs for the stochastic PDE system. The main advantage of the quantized control law lies in reducing the energy that the system spends. The stability analysis is nontrivial due to the complex stochastic PDE model. Different stability results are presented for each case. Sufficient LMI-based conditions are investigated to ensure the internal mean-square exponential stability and H-infinity performance of the perturbed actuated system. Consistent simulation results that support the proposed theoretical statements are provided.

关键词： H-infinity control quantized control stochastic distributed parameter systems

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Identification and adaptive control of some stochastic distributed parameter systems

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INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING 2001年第6期15卷 565-587页

作者： Pasik-Duncan, B Univ Kansas Dept Math Lawrence KS 66045 USA

An important class of controlled linear stochastic distributed parameter systems is that with boundary or point control. A survey of some existing adaptive control problems with their solutions for the boundary or the point control of a partially known linear stochastic distributed parameter systems is presented. The distributed parameter system is described by an analytic semigroup with cylindrical white noise and a control that occurs only on the boundary or at discrete points. The unknown parameters in the model appear affinely in both the infinitesimal generator of the semigroup and the linear transformation of the control. The noise in the system is a cylindrical white Gaussian noise. Strong consistency is verified for a family of least-squares estimates of the unknown parameters. For a quadratic cost functional of the state and the control, the certainty equivalence control is self-optimizing, that is the family of average costs converges to the optimal ergodic cost. Copyright (C) 2001 John Wiley & Sons, Ltd.

关键词： identification adaptive control stochastic distributed parameter systems

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