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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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control design for non-linear distributed parameter systems with mobile actuators and sensors

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IET Control Theory & Applications 2019年第14期13卷 2228-2238页

作者： Xiao-Wei Zhang Huai-Ning Wu The Science and Technology on Aircraft Control Laboratory School of Automation Science and Electrical Engineering Beihang University (Beijing University of Aeronautics and Astronautics) Beijing 100191 People's Republic of China

This study deals with the control design problem for a class of non-linear distributed parameter systems described by parabolic partial differential equations (PDEs) via mobile collocated actuators and sensors. Initially, the spatial domain is decomposed into multiple subdomains according to the number of actuator/sensor pairs and the projection modification algorithm is employed to guarantee each actuator/sensor pair is only capable of moving within the respective subdomain. Subsequently, the well-posedness of the closed-loop PDE system is analysed by means of the operator semigroup theory. Then, a control-plus-guidance design method for the non-linear PDE system is developed in the form of bilinear matrix inequalities, such that the resulting closed-loop system is exponentially stable while satisfying a prescribed performance of disturbance attenuation, and the mobile actuator/sensor guidance can enhance the transient performance of the closed-loop system. Finally, a numerical example and a practical application example are respectively given to show the effectiveness of the proposed design method.

关键词： closed loop systems distributed parameter systems parabolic equations sensors partial differential equations nonlinear control systems control system synthesis actuators nonlinear distributed parameter systems mobile actuators control design problem parabolic partial differential equations mobile collocated actuators actuator/sensor pair closed-loop PDE system control-plus-guidance design method nonlinear PDE system resulting closed-loop system mobile actuator/sensor guidance

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A PD-Type Iterative Learning Algorithm for Semi-Linear distributed parameter systems With Sensors/Actuators

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IEEE ACCESS 2019年 7卷 159037-159047页

作者： Zhang, Jianxiang Cui, Baotong Jiang, Zhengxian Chen, Juan Jiangnan Univ Sch Internet Things Engn Minist Educ Key Lab Adv Proc Control Light Ind Wuxi 214122 Jiangsu Peoples R China Jiangnan Univ Sch Sci Wuxi 214122 Jiangsu Peoples R China Tallinn Univ Technol Dept Comp Syst EE-19086 Tallinn Estonia

In this paper, the control problem of semi-linear distributed parameter system (DPS) with sensors/actuators is considered using iterative learning control (ILC) method. During the learning process, the output signals of the system exist random data dropout which is described as a Bernoulli random variable. Then, a novel intermittent updating PD-type ILC algorithm is proposed on the basis of the available output information. In this kind ILC algorithm, the scheme only updates its control signal when the output signal is successfully transmitted. Hence, the intermittent updating PD-type ILC algorithm is presented for a semi-linear parabolic DPS based on single sensor and single actuator, and the convergence condition of the output error is obtained by using Bellman-Gronwall lemma and semigroup theory under some given assumptions. Secondly, this kind PD-type ILC law is extended to control the semi-linear DPS with multiple sensors and multiple actuators. Lastly, one example is given to demonstrate the effectiveness of the proposed scheme.

关键词： distributed parameter systems Actuators Convergence Graphical models Distribution functions Robot sensing systems Boundary conditions distributed parameter systems learning systems intelligent control sensors actuators

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Empirical Gramian-based spatial basis functions for model reduction of nonlinear distributed parameter systems

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MATHEMATICAL AND COMPUTER MODELLING OF DYNAMICAL systems 2018年第3期24卷 258-274页

作者： Jiang, Mian Wu, Jigang Zhang, Wenan Li, Xuejun Hunan Univ Sci & Technol Hunan Prov Key Lab Hlth Maintenance Mech Equipmen Xiangtan 411201 Peoples R China Hunan Univ Sci & Technol Engn Res Cent Adv Min Equipment Minist Educ Xiangtan Peoples R China

Correct selection of spatial basis functions is crucial for model reduction for nonlinear distributed parameter systems in engineering applications. To construct appropriate reduced models, modelling accuracy and computational costs must be balanced. In this paper, empirical Gramian-based spatial basis functions were proposed for model reduction of nonlinear distributed parameter systems. Empirical Gramians can be computed by generalizing linear Gramians onto nonlinear systems, which results in calculations that only require standard matrix operations. Associated model reduction is described under the framework of Galerkin projection. In this study, two numerical examples were used to evaluate the efficacy of the proposed approach. Lower-order reduced models were achieved with the required modelling accuracy compared to linear Gramian-based combined spatial basis function- and spectral eigenfunction-based methods.

关键词： distributed parameter systems model reduction spatial basis functions empirical balanced truncation

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Adaptive H∞ Consensus Control for distributed parameter systems of Hyperbolic Type on Directed Graph

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IFAC-PapersOnLine 2018年第23期51卷 307-312页

作者： Miyasato, Yoshihiko The Institute of Statistical Mathematics TachikawaTokyo190-8562 Japan

A design method of adaptive H∞ consensus control of multi-agent systems composed of a class of infinite-dimensional systems on directed network graphs, is presented in this paper. The proposed control scheme is derived as a solution of certain H∞ control problems, where the effects of neglected infinite-dimensional modes are regarded as external disturbances to the process. It is shown that the desirable consensus tracking is achieved approximately via the finite dimensional adaptive controller. © 2018

关键词： Adaptive control systems Directed graphs distributed parameter control systems Intelligent control Multi agent systems Adaptive Control Adaptive controllers Consensus control distributed parameter systems External disturbances Finite dimensional Infinite dimensional Infinite dimensional system

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ANALYSIS OF THE ERROR IN AN ITERATIVE ALGORITHM FOR ASYMPTOTIC REGULATION OF LINEAR distributed parameter CONTROL systems

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ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE 2019年第5期53卷 1577-1606页

作者： Aulisa, Eugenio Gilliam, David S. Pathiranage, Thanuka W. Texas Tech Univ Dept Math & Stat Lubbock TX 79409 USA Univ Kelaniya Dept Math Kelaniya Sri Lanka

Applications of regulator theory are ubiquitous in control theory, encompassing almost all areas of systems and control engineering. Examples include active noise suppression [Banks et al., Decision and Control, Active Noise Control: Piezoceramic Actuators in Fluid/structure Interaction Models, IEEE, Los Alamitos, CA (1991) 2328-2333], design and control of energy efficient buildings [Borggaard et al., Control, Estimation and Optimization of Energy Efficient Buildings. Riverfront, St. Louis, MO (2009) 837-841.] and control of heat exchangers [Aulisa et al., IFAC-PapersOnLine 49 (2016) 104-109.]. Numerous other examples can be found in [Aulisa and Gilliam, A Practical Guide to Geometric Regulation for distributed parameter systems. Chapman and Hall/CRC, Boca Raton (2015).]. In the geometric approach to asymptotic regulation the main object of interest is a pair of operator equations called the regulator equations, whose solution provides a control solving the tracking/disturbance rejection regulation problem. In this paper we present an iterative algorithm, called the beta-iteration method, which is based on the geometric methodology, and delivers accurate control laws for approximate asymptotic regulation. This iterative scheme has been successfully applied to a wide range of linear and nonlinear multi-physics examples and in practice only one or two iterations are usually required to deliver sufficiently accurate results. One drawback to these research efforts is that no proof was given of the convergence of the method. This work contains a detailed analysis of the error in the iterative scheme for a large class of linear distributed parameter systems. In particular we show that the iterative errors converge at a geometric rate. We demonstrate our estimates on three control problems in multi-physics applications.

关键词： Regulator problem distributed parameter systems geometric control dynamic regulator equations iterative numerical algorithm

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Remarks on Functional Observers for distributed parameter systems 23

Remarks on Functional Observers for Distributed Parameter Sy...

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23rd International Conference on Methods and Models in Automation and Robotics (MMAR)

作者： Emirsajlow, Zbigniew West Pomeranian Univ Technol Dept Control & Measurements Sikorskiego 37 PL-70313 Szczecin Poland

ISBN: (纸本)9781538643259

The paper deals with the output observation problem for a class of distributed parameter systems. We describe the design procedure by deriving sufficient conditions to be satisfied by a functional observer which does the job. The plant is described by a state space model with the system operator generating a strongly continuous group. We assume that both the input and the output operators of the plant and the observer are bounded.

关键词： Observers Mathematical model Generators distributed parameter systems Analytical models Electronic mail Hilbert space

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Observer-based feedback stabilization of distributed parameter systems of parabolic type with non-self-adjoint operators

Observer-based feedback stabilization of distributed paramet...

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Asian Control Conference

作者： Yoshiyuki Tsutsui Yoshihiko Miyasato Department of Statistical Science School of Multidisciplinary Sciences The Graduate University for Advanced Studies Kanagawa Japan Department of Statistical Modeling The Institute of Statistical Mathematics Tokyo Japan

ISBN: (纸本)9781728102634

This paper deals with a finite-dimensional feedback stabilization of distributed parameter systems of parabolic type with a non-self-adjoint system operator. When the system operator is self-adjoint as well studied in the previous literature, a finite dimensional feedback stabilizer with a prescribed exponential decay rate can be constructed. It is shown that, even in the case of a non-self-adjoint operator, a similar design method can be applied under some additional assumptions. The controller contains a finite-dimensional observers which can estimate the ill-behaved modes of the plant even under the effect of spillovers.

关键词： Observers Eigenvalues and eigenfunctions distributed parameter systems Adaptive control Feeds Design methodology Heating systems

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Observer Design for Boundary Coupled Fractional Order distributed parameter systems

Observer Design for Boundary Coupled Fractional Order Distri...

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International Conference on Control, Mechatronics and Automation (ICCMA)

作者： Yanjiu ZHOU Juan CHEN Baotong CUI Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education) School of IoT Engineering Jiangnan University Wuxi China Department of Computer Systems Tallinn University of Technology Tallinn Estonia

This paper studies the observer design for the fractional order boundary coupled distributed parameter systems. Firstly, we obtain the decoupled observer error systems from the state system and observer system. Secondly, the advection terms are eliminated through the invertible transformation and we can obtain the general reaction-diffusion partial differential equations, which are more convenient for discussions. Thirdly, Backstepping method and target systems are employed to give kernel partial differential equations and then the related observer gains can be derived from the corresponding kernels. Finally, Mittag-Leffler stability of the designed fractional order observers is analyzed and the main results are illustrated by the simulation graphically.

关键词： control nonlinearities distributed parameter systems observers partial differential equations reaction-diffusion systems stability

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Data-Driven Nonlinear Optimal Control for distributed parameter systems with Output Delay

Data-Driven Nonlinear Optimal Control for Distributed Parame...

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6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control (LHMNC)

作者： Nishida, Gou Sakamoto, Noboru Nihon Univ Coll Engn Dept Elect & Elect Engn 1 Nakagawara Koriyama Fukushima 9638642 Japan Nanzan Univ Fac Sci & Engn Dept Mechatron Shyowa Ku 18 Yamazato Cho Nagoya Aichi 4668673 Japan

This paper presents a predictive nonlinear optimal control method for nonlinear distributed parameter systems with output delay by means of a data-driven modeling method called the dynamic mode decomposition. Nonlinear optimal control problems can be solved by an exact numerical solver of Hamilton-Jacobi equations called the stable manifold method. A nonlinear optimal control for distributed parameter systems has been proposed in terms of a finite-dimensional reduction derived from time series data of system responses. The optimal controllers consist of optimal gains at each state on an optimal orbit. Thus, output delays bring on the mismatch between gains calculated from observations and actual states of controlled systems. A state prediction realized by the dynamic mode decomposition can recover a performance degradation arisen from the delay. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Optimal control Nonlinear control distributed parameter systems

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