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Finite-dimensional guaranteed cost sampled-data fuzzy control of Markov jump distributed parameter systems via T-S fuzzy model

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IET CONTROL THEORY AND APPLICATIONS 2018年第15期12卷 2098-2108页

作者： Ji, Huihui Zhang, He Cui, Baotong Jiangnan Univ Sch Internet Things Engn Key Lab Adv Proc Control Light Ind Minist Educ Wuxi 214122 Peoples R China Nanjing Univ Sci & Technol Sch Automat Nanjing Jiangsu Peoples R China

In this study, the authors are concerned with a finite-dimensional guaranteed cost sampled-data fuzzy control problem, which is addressed for a class of non-linear Markov jump parabolic partial differential equation (MJPPDE) systems. Applying the Galerkin's method to the MJPPDE system, a non-linear Markov jump ordinary differential equation (MJODE) system is derived. The resulting non-linear MJODE system can describe the dominant dynamics of the MJPPDE system, which is subsequently expressed by the Takagi-Sugeno (T-S) fuzzy model. Then, a guaranteed cost sampled-data fuzzy controller is developed to stabilise the closed-loop slow fuzzy system exponentially in the mean-square sense while providing an upper bound for the quadratic cost function. Making full use of their special features, they will be able to establish the bound on t. The authors' theory enables us to guarantee the existence of the feedback controller and to judge the effectiveness of the feedback control based on the sampled-data to stabilise the given system in the sense of mean-square exponential stability.

关键词： fuzzy systems linear matrix inequalities Lyapunov methods fuzzy control differential equations Markov processes partial differential equations sampled data systems nonlinear control systems feedback asymptotic stability distributed parameter systems stochastic systems stability control system synthesis closed loop systems finite-dimensional guaranteed cost sampled-data nonlinear Markov jump parabolic partial differential equation systems MJPPDE system nonlinear Markov jump ordinary differential equation system resulting nonlinear MJODE system Takagi-Sugeno fuzzy model closed-loop slow fuzzy system quadratic cost function feedback controller feedback control given system -dimensional guaranteed cost sampled-data Markov jump distributed parameter systems T-S fuzzy model

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Spreadability and vulnerability of distributed parameter systems

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INTERNATIONAL JOURNAL OF systems SCIENCE 2007年第4期38卷 305-317页

作者： Bernoussi, A. Fac Sci & Tech Dept Math Tanger Morocco

In this article we focus on the mathematical development of vulnerability concept and vulnerability index and analyze the dependence of the vulnerability concept definition on that of spreadability [A. El Jai and K. Kassara, "Spreadable distributed systems", Mathem. and Comp. model., 20, pp. 47-64, 1994;A. Bernoussi and A. El Jai, "New approach of spread ability", Journal of Mathematical and Computer Modelling 31, pp 93-109, 2000;A. Bernoussi, A. El Jai and A. J. Pritchard, "Spreadability and evolving interfaces", Inter. J. Syst. Sci., 32, pp. 1217-1232, 2001]. It is found that the mathematical approach of the vulnerability concept is rather attractive and can be applied to many engineering problems. To illustrate this, some examples and applications are considered.

关键词： distributed parameter systems spreadability vulnerability

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Stabilization for Markovian Jump distributed parameter systems With Time Delay

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IEEE ACCESS 2019年 7卷 103931-103937页

作者： Li, Yanbo Chen, Chaoyang Wang, Baoxian Guangxi Univ Finance & Econ Sch Informat & Stat Nanning 530001 Peoples R China Hunan Univ Sci & Technol Sch Informat & Elect Engn Xiangtan 411201 Peoples R China Boston Univ Ctr Polymer Studies Boston MA 02215 USA Boston Univ Dept Phys 590 Commonwealth Ave Boston MA 02215 USA China Three Gorges Univ Coll Sci Yichang 443002 Peoples R China

The problems of stochastic stability and stabilization for a class of Markovian jump distributed parameter systems with time delay are researched in this paper. First, taking advantage of a combination of Poincare inequality and Green formula, a stochastic stability criterion is presented by a linear matrix inequality (LMI) approach. Then, a state feedback controller is designed. Based on the proposed results, the sufficient conditions of the close-loop system's stochastic stability are given in terms of a set of LMIs by constructing the appropriate Lyapunov functionals, calculating the weak infinitesimal generator, and using the Schur complement lemma. The sufficient conditions could be solved directly and applied to engineering practice conveniently. The obtained results generalize and enrich the theory of distributed parameter systems with time delay. The model of Markovian jump distributed parameter systems is more fitting the actual system's requirements and has wider application scope. Finally, numerical examples are used to demonstrate the validity of the method.

关键词： Markovian jump distributed parameter systems stochastic stability linear matrix inequality

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An approach to the selection of optimal sensor locations in distributed parameter systems

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JOURNAL OF PROCESS CONTROL 2000年第4期10卷 291-300页

作者： Vande Wouwer, A Point, N Porteman, S Remy, M Fac Polytech Mons Lab Automat B-7000 Mons Belgium

This paper presents an approach to the selection of optimal sensor locations in distributed parameter systems, which distinguishes the purposes of state estimation from the purposes of parameter estimation. In the first case, the optimality criterion is based on a measure of independence between the sensor responses, while in the second case, it is based on a measure of independence between the parameter sensitivity functions. The procedure, which is general and can be applied to models with any degree of complexity, is illustrated with the optimal placement of temperature sensors in a catalytic fixed-bed reactor. Some numerical results for the on-line estimation of temperature and concentration profiles as well as for the estimation of unknown model parameters are discussed. (C) 2000 Elsevier Science Ltd. All rights reserved.

关键词： experiment design parameter estimation state estimation nonlinear observers distributed parameter systems

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IDENTIFICATION OF distributed parameter-systems VIA MULTIDIMENSIONAL DISTRIBUTIONS

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IEE PROCEEDINGS-D CONTROL THEORY AND APPLICATIONS 1980年第2期127卷 45-50页

作者： SAHA, DC RAO, GP Department of Electrical Engineering Indian Institute of Technology Kharagpur India

The paper presents a method of determining the parameters of a process described by a partial differential equation from a knowledge of its solution. The development is based on treating the process signals as multidimensional distributions in the manner established by Laurent Schwartz, and expanding them in an exponentially weighted series of the generalised partial derivatives of the multidimensional Dirac delta function, termed as the Poisson moment functional ( p. m. f. ) expansion. The ability of the method is successfully demonstrated in the presence of noise.

关键词： Simulation, modelling and identification distributed parameter systems multidimensional distributions partial differential equation distributed parameter control systems identification

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Optimal switching policy for performance enhancement of distributed parameter systems based on event-driven control

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Chinese Physics B 2014年第7期23卷 211-217页

作者：穆文英崔宝同楼旭阳李纹 Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education) Jiangnan University

This paper aims to improve the performance of a class of distributed parameter systems for the optimal switching of actuators and controllers based on event-driven control. It is assumed that in the available multiple actuators, only one actuator can receive the control signal and be activated over an unfixed time interval, and the other actuators keep dormant. After incorporating a state observer into the event generator, the event-driven control loop and the minimum inter-event time are ultimately bounded. Based on the event-driven state feedback control, the time intervals of unfixed length can be obtained. The optimal switching policy is based on finite horizon linear quadratic optimal control at the beginning of each time subinterval. A simulation example demonstrate the effectiveness of the proposed policy.

关键词： distributed parameter systems optimal switching policy event-driven

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Observer-based dynamic event-triggered control for distributed parameter systems over mobile sensor-plus-actuator networks

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Chinese Physics B 2024年第4期33卷 237-243页

作者：穆文英庄波邱芳 Shandong Engineering Research Center of Aeronautical Materials and Devices Shangdong University of AeronauticsBinzhou 256600China School of Information Engineering Shangdong University of AeronauticsBinzhou 256600China School of Science Shangdong University of AeronauticsBinzhou 256600China

We develop a policy of observer-based dynamic event-triggered state feedback control for distributed parameter systems over a mobile sensor-plus-actuator *** is assumed that the mobile sensing devices that provide spatially averaged state measurements can be used to improve state estimation in the *** the purpose of decreasing the update frequency of controller and unnecessary sampled data transmission, an efficient dynamic event-triggered control policy is *** an event-triggered system, when an error signal exceeds a specified time-varying threshold, it indicates the occurrence of a typical *** global asymptotic stability of the event-triggered closed-loop system and the boundedness of the minimum inter-event time can be *** on the linear quadratic optimal regulator, the actuator selects the optimal displacement only when an event occurs.A simulation example is finally used to verify that the effectiveness of such a control strategy can enhance the system performance.

关键词： distributed parameter systems event-triggered control mobile sensors mobile actuators

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On the Lyapunov-based second-order SMC design for some classes of distributed parameter systems

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IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION 2012年第4期29卷 437-457页

作者： Orlov, Yury Pisano, Alessandro Scodina, Stefano Usai, Elio Univ Cagliari Dept Elect & Elect Engn Cagliari Italy CICESE Res Ctr Ensenada Baja California Mexico

This paper addresses the Lyapunov-based design of second-order sliding mode controllers in the domain of distributed parameter systems (DPSs). To the best of our knowledge, the recent authors' publications (Orlov et al., 2010, Continuous state-feedback tracking of an uncertain heat diffusion process. Syst. Control Lett., 59, 754-759;Orlov et al., 2011, Exponential stabilization of the uncertain wave equation via distributed dynamic input extension. IEEE Trans. Autom. Control, 56, 212-217;Pisano et al., 2011, Tracking control of the uncertain heat and wave equation via power-fractional and sliding-mode techniques. SIAM J. Control Optim., 49, 363-382) represent the seminal applications of second-order sliding mode control techniques to DPSs. A Lyapunov-based framework of analysis was found to be appropriate in the above publications. While reviewing the main existing results in this new field of investigation, the paper provides the novelty as well and gives several hints and perspectives for the generalization, listing some open problems.

关键词： distributed parameter systems heat equation wave equation second-order sliding mode control Lyapunov analysis

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Sampled-data fuzzy control for a class of nonlinear parabolic distributed parameter systems under spatially point measurements

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FUZZY SETS AND systems 2019年 374卷 60-81页

作者： Wang, Zi-Peng Li, Han-Xiong Wu, Huai-Ning Univ Jinan Sch Elect Engn Jinan 250022 Shandong Peoples R China Cent South Univ State Key Lab High Performance Complex Mfg Changsha Hunan Peoples R China City Univ Hong Kong Dept Syst Engn & Engn Management Hong Kong Peoples R China Beihang Univ Sch Automat Sci & Elect Engn Sci & Technol Aircraft Control Lab Beijing 100191 Peoples R China

In this paper, the exponential stabilization problem is addressed for a class of nonlinear parabolic partial differential equation (PDE) systems via sampled-data fuzzy control approach. Initially, the nonlinear PDE system is accurately represented by the Takagi-Sugeno (T-S) fuzzy PDE model. Then, based on the T-S fuzzy PDE model, a novel time-dependent Lyapunov functional is used to design a sampled-data fuzzy controller under spatially point measurements such that the closed-loop fuzzy PDE system is exponentially stable with a given decay rate. The stabilization conditions are presented in terms of a set of linear matrix inequalities (LMIs). Finally, simulation results on the control of the diffusion equation and the FitzHugh-Nagumo (FHN) equation to illustrate the effectiveness of the proposed design method. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Exponential stability Sampled-data control Fuzzy control distributed parameter systems Linear matrix inequality (LMI)

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Modal consensus observers for distributed parameter systems

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 2022年第1期32卷 472-497页

作者： Demetriou, Michael A. Worcester Polytech Inst Aerosp Engn Dept Worcester MA 01609 USA

This article proposes a new type of a consensus protocol for the synchronization of distributed observers in systems governed by parabolic partial differential equations. Addressing the goal of sharing useful information among distributed observers, it delves into the details governing the modal decompositions of distributed parameter systems. Assuming that two different groups of sensors are available to provide process information to the two distributed observers, the proposed modal consensus design ensures that only useful information is transmitted to the requisite modal components of each of the observers. Without any consensus protocol, the observers capture different frequency content of the spatial process in differing degrees, as it relates to the concept of modal observability. Their modal components exhibit different learning behavior toward the process state. In the extreme case, it turns out that certain modal components of the distributed observers occasionally behave as naive observers. To ensure that, both collectively and modal componentwise, the observers agree both with the process state and with each other, a modal component consensus protocol is proposed. Such a consensus protocol is mono-directional and provides only useful information necessary to the appropriate modal component of the distributed filters that behaves as a naive modal observer. This protocol, when abstracted and applied to different state decompositions can be viewed as mono-directional projections of information transmitted and received by the participating distributed observers. Detailed numerical studies of advection PDE in one and two spatial dimensions are included to elucidate the details of the proposed modal consensus observers.

关键词： distributed parameter systems modal consensus modal decompositions synchronization

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