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On PID Control Theory for Nonaffine Uncertain stochastic systems

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Journal of systems Science & Complexity 2023年第1期36卷 165-186页

作者： ZHANG Jinke ZHAO Cheng GUO Lei Key Laboratory of systems and Control Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Science University of Chinese Academy of SciencesBeijing 100049China

PID(proportional-integral-derivative)control is recognized to be the most widely and successfully employed control strategy by ***,there are limited theoretical investigations explaining the rationale why PID can work so well when dealing with nonlinear uncertain *** paper continues the previous researches towards establishing a theoretical foundation of PID control,by studying the regulation problem of PID control for nonaffine uncertain nonlinear stochastic *** be specific,a three dimensional parameter set will be constructed explicitly based on some prior knowledge on bounds of partial derivatives of both the drift and diffusion *** will be shown that the closed-loop control system will achieve exponential stability in the mean square sense under PID control,whenever the controller parameters are chosen from the constructed parameter ***,similar results can also be obtained for PD(PI)control in some special cases.A numerical example will be provided to illustrate the theoretical results.

关键词： Asymptotically regulation global stability nonaffine PID control stochastic systems uncertain structure

Integral sliding mode control design for nonlinear stochastic systems under imperfect quantization

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Science China(Information Sciences) 2017年第12期60卷 71-81页

作者： Yabin GAO Wensheng LUO Jianxing LIU Ligang WU Research Institute of Intelligent Control and systems Harbin Institute of Technology

This paper presents a sliding mode control(SMC) scheme via output-feedback approach for It?o stochastic systems under a quantization mechanism. The quantization process is formulated with the imperfection that random packet loss occurs at the logarithmic quantizer. A Luenberger observer is designed, based on the packet loss rate and the imperfect quantized measurement. A novel SMC law is synthesized by utilization of an integral sliding surface. The stochastic stability of the resulting closed-loop system is analyzed in terms of Lyapunov stability, and a set of solvable matrix inequalities are established for practical application requirements. Finally, a simulation example is employed for the illustration of the effectiveness of the presented control scheme.

关键词： stochastic systems quantized control sliding mode control observer design packet loss

Stability analysis for semi-Markovian switched stochastic systems with asynchronously impulsive jumps

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Science China(Information Sciences) 2021年第1期64卷 162-174页

作者： Xiaowu MU Zenghui HU School of Mathematics and Statistics Zhengzhou University

The almost surely(a.s.) exponential stability is studied for semi-Markovian switched stochastic systems with randomly impulsive jumps. We start from the case that switches and impulses occur synchronously, in which the impulsive switching signal is a semi-Markovian process. For the case that switches and impulses occur asynchronously, the impulsive arrival time sequence and the types of jump maps are driven by a renewal process and a Markov chain, respectively. By applying the multiple Lyapunov function approach, sufficient conditions of exponential stability a.s. are obtained based upon the ergodic property of semi-Markovian process. The validity of the proposed theoretical results is demonstrated by a numerical example.

关键词： stochastic systems multiple Lyapunov function almost surely exponential stability impulsive jumps semi-Markovian switching renewal process

Stabilization for Discrete-Time stochastic systems with Multiple Input Delays

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Journal of systems Science & Complexity 2023年第5期36卷 1961-1980页

作者： LI Lin ZHANG Huanshui College of Mechanical and Electronic Engineering Shandong Agricultural UniversityTaian 271018China School of Information Science and Engineering Shandong Agricultural UniversityTaian 271018China College of Electrical Engineering and Automation Shandong University of Science and TechnologyQingdao 266590China

A stabilization problem for stochastic systems with multiple input delays is investigated herein.A new method to construct an optimal control problem with input constraints is adopted.A sufficient stabilization condition is established via Riccati-type equations,whose verification is computationally simple because the variable dimension of the equations does not increase with regard to the delay.A stabilization controller is proposed,and it is a feedback of the state and a history *** controller uses less history information than those with distributed *** numerical examples illustrate the effectiveness of the obtained results.

关键词： Riccati-type equations stabilization stochastic systems time-delay systems

Shape control on probability density function in stochastic systems

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Journal of systems Engineering and Electronics 2014年第1期25卷 144-149页

作者： Lingzhi Wang Fucai Qian Jun Liu School of Automation and Information Xi'an University of Technology School of Automation Xi'an University of Posts and Telecommunications State Key Laboratory for Manufacturing systems Engineering Xi'an Jiaotong University

A novel strategy of probability density function （PDF） shape control is proposed in stochastic systems. The control er is designed whose parameters are optimal y obtained through the improved particle swarm optimization algorithm. The parameters of the control er are viewed as the space position of a particle in particle swarm optimization algorithm and updated continual y until the control er makes the PDF of the state variable as close as possible to the expected PDF. The proposed PDF shape control technique is compared with the equivalent linearization technique through simulation experiments. The results show the superiority and the effectiveness of the proposed method. The control er is excellent in making the state PDF fol ow the expected PDF and has the very smal error between the state PDF and the expected PDF, solving the control problem of the PDF shape in stochastic systems effectively.

关键词： stochastic systems probability density function (PDF),shape control improved particle swarm optimization.

Frequency Resonance in stochastic systems

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Chinese Physics Letters 2003年第2期20卷 202-205页

作者：钱敏张雪娟 LMAN SchoolofMathematicalSciencesPekingUniversityBeijing100871 ShaoxingCollegeofArtsandSciences Shaoxing312000

The phenomenon of frequency resonance, which is usually related to deterministic systems, is investigated in stochastic systems. We show that for those autonomous systems driven only by white noise, if the output power spectrum exhibits a nonzero peak frequency, then applying a periodic signal just on this noise-induced central frequency can also induce a resonance phenomenon, which we call the frequency stochastic resonance. The effect of such a resonance in a coupled stochastic system is shown to be much better than that in a single-oscillator system.

关键词： stochastic systems

Robust sliding mode control of general time-varying delay stochastic systems with structural uncertainties

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Control Theory and Technology 2014年第4期12卷 357-367页

作者： Sheng-Guo WANG Libin BAI Mingzhi CHEN Department of Engineering Technology and Department of Software and Information systems (Graduate Faculty) University of North Carolina at Charlotte (UNC Charlotte) Department of Software and Information systems UNC Charlotte NC 28223-0001 U.S.A. College of Mathematics and Computer Science Fuzhou University

This paper presents a new robust sliding mode control （SMC） method with well-developed theoretical proof for general uncertain time-varying delay stochastic systems with structural uncertainties and the Brownian noise （Wiener process）. The key features of the proposed method are to apply singular value decomposition （SVD） to all structural uncertainties and to introduce adjustable parameters for control design along with the SMC method. It leads to a less-conservative condition for robust stability and a new robust controller for the general uncertain stochastic systems via linear matrix inequality （LMI） forms. The system states are able to reach the SMC switching surface as guaranteed in probability 1. Furthermore, it is theoretically proved that the proposed method with the SVD and adjustable parameters is less conservatism than the method without the SVD. The paper is mainly to provide all strict theoretical proofs for the method and results.

关键词： Robust control Time-varying delay systems stochastic systems Lyapunov methods Sliding mode control Time-varying systems

The p-moment exponential robust stability for stochastic systems with distributed delays and interval parameters

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Applied Mathematics and Mechanics(English Edition) 2009年第7期30卷 915-924页

作者：苏春华刘思峰 College of Economics and Management Nanjing University of Aeronautics andAstronautics College of Mathematics and Information Science Xinyang Normal University

The p-moment exponential robust stability for stochastic systems with distributed delays and interval parameters is studied. By constructing the Lyapunov- Krasovskii functional and employing the decomposition technique of interval matrix and Ito＇s formula, the delay-dependent criteria for the p-moment exponential robust stability are obtained. Numerical examples show the validity and practicality of the presented criteria.

关键词： interval matrix stochastic systems distributed delays robust stability

Guaranteed Quadratic Stabilization of Certain Time-Varying Large-Scale Delay It stochastic systems

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Journal of systems Engineering and Electronics 2000年第3期11卷 35-39页

作者： Jin Yansheng & Xu Yumin (Dept. of Mathematics and Physics, Yanshan University, Qinhuangdao 066004, P. R. China) Deng Feiqi (Dept. of Automatic Control Engineering, South China University of Technology, Guangzhou 510641, P. R. China) Dept. of Mathematics and Physics Yanshan University Qinhuangdao 066004 P. R. China Dept. of Automatic Control Engineering South China University of Technology Guangzhou 510641 P. R. China

In this paper, we investigate the decentralized stabilization of some time-varying uncertain large-scale stochastic systems with delays under matching conditions. A type of decentralized controllers with guaranteed s... 详细信息

关键词： stochastic systems Uncertainty Stabilization.