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Fuzzy Intermittent Extended Dissipative Control for Delayed distributed parameter systems With Stochastic Disturbance: A Spatial Point Sampling Approach

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IEEE TRANSACTIONS ON FUZZY systems 2022年第6期30卷 1734-1749页

作者： Ding, Kui Zhu, Quanxin Hunan Normal Univ Sch Math & Stat MOE LCSM Changsha 410081 Peoples R China Nanjing Normal Univ Sch Math Sci Nanjing 210023 Peoples R China Nanjing Normal Univ Inst Finance & Stat Nanjing 210023 Peoples R China Chengdu Univ Sch Informat Sci & Engn Chengdu 610106 Peoples R China

In this article, the extended dissipative performance of distributed parameter systems (DPSs) with stochastic disturbances and multiple time-varying delays is studied by using a new fuzzy aperiodic intermittent sampled-data control strategy. Different from the previous fuzzy sampled-data control results, the state sampling of the proposed sampled-data controller occurs only in space and is intermittent rather than continuous in the time domain. By introducing a novel multitime-delay-dependent switched Lyapunov functional to explore the dynamic characteristics of the controlled system, and by means of the famous Jensen's inequality with reciprocally convex approach, Wirtinger's inequality, the criterion of the system's mean square stabilization is established based on the LMI technique, which quantitatively reveals the relationship between the control period, the control length, and the upper bound of the control sampling interval. Especially, the optimal control gain is given by designing an optimized algorithm in the article, which greatly reduces the cost. Finally, two numerical examples are presented to demonstrate the effectiveness and superiority of the proposed approach.

关键词： Actuators Control systems Delays Time-varying systems Aerospace electronics Switches distributed parameter systems distributed parameter systems (DPSs) extended dissipative performance fuzzy aperiodic intermittent sampled-data control optimization algorithm stochastic disturbances

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An account of chronological developments in control of distributed parameter systems

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ANNUAL REVIEWS IN CONTROL 2009年第1期33卷 59-68页

作者： Padhi, Radhakant Ali, Sk. Faruque Indian Inst Sci Dept Aerosp Engn Bangalore 560012 Karnataka India Indian Inst Sci Dept Civil Engn Bangalore 560012 Karnataka India

Control systems arising in many engineering fields are often of distributed parameter type, which are modeled by partial differential equations. Decades of research have lead to a great deal of literature on distributed parameter systems scattered in a wide spectrum. Extensions of popular finite-dimensional techniques to infinite-dimensional systems as well as innovative infinite-dimensional specific control design approaches have been proposed. A comprehensive account of all the developments would probably require several volumes and is perhaps a very difficult task. In this paper, however, an attempt has been made to give a brief yet reasonably representative account of many of these developments in a chronological order. To make it accessible to a wide audience, mathematical descriptions have been completely avoided with the assumption that an interested reader can always find the mathematical details in the relevant references. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Partial differential equations distributed parameter systems Review Control Infinite dimensional systems

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Trajectory planning for quasilinear parabolic distributed parameter systems based on finite-difference semi-discretisations

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INTERNATIONAL JOURNAL OF CONTROL 2010年第6期83卷 1093-1106页

作者： Utz, T. Meurer, T. Kugi, A. Vienna Univ Technol Automat & Control Inst A-1040 Vienna Austria

In this contribution, a flatness-based approach is considered for the solution of the trajectory planning problem for quasilinear parabolic distributed parameter systems (DPS) by making use of finite-difference semi-discretisations. It is shown that the method yields solutions which are equivalent to results known from the infinite-dimensional trajectory planning for a certain class of quasi-linear parabolic DPS. Furthermore, the methodology being proposed can also be applied to systems with general analytic nonlinearities. As analytical convergence results are not available in this case, a numerical test criterion for the convergence behaviour is suggested.

关键词： trajectory planning differential flatness distributed parameter systems finite-difference semi-discretisation diffusion-convection-reaction systems

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On the control of distributed parameter systems using a multidimensional systems setting

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MECHANICAL systems AND SIGNAL PROCESSING 2008年第7期22卷 1566-1581页

作者： Cichy, Blazej Augusta, Petr Rogers, Eric Galkowski, Krzysztof Hurak, Zdenek Univ Southampton Sch Elect & Comp Sci Southampton SO17 1BJ Hants England Univ Zielona Gora Inst Control & Computat Engn PL-65246 Zielona Gora Poland Acad Sci Czech Republic Inst Informat Theory & Automat CR-18208 Prague Czech Republic Czech Tech Univ Dept Control Engn Prague 12135 Czech Republic

The unique characteristic of a repetitive process is a series of sweeps, termed passes, through a set of dynamics defined over a finite duration with resetting before the start of the each new one. On each pass an output, termed the pass profile is produced which acts as a forcing function on, and hence contributes to, the dynamics of the next pass profile. This leads to the possibility that the output, i.e. the sequence of pass profiles, will contain oscillations which increase in amplitude in the pass-to-pass direction. Such behavior cannot be controlled by standard linear systems approach and instead they must be treated as a multidimensional system, i.e. information propagation in more than one independent direction. Physical examples of such processes include long-wall coal cutting and metal rolling. In this paper, stability analysis and control systems design algorithms are developed for a model where a plane, or rectangle, of information is propagated in the pass-to-pass direction. The possible use of these in the control of distributed parameter systems is then described using a fourth-order wavefront equation. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： distributed parameter systems modelling control law design

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Adaptive Neural Control Design for Nonlinear distributed parameter systems With Persistent Bounded Disturbances

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IEEE TRANSACTIONS ON NEURAL NETWORKS 2009年第10期20卷 1630-1644页

作者： Wu, Huai-Ning Li, Han-Xiong Beihang Univ Sch Automat Sci & Elect Engn Beijing 100191 Peoples R China City Univ Hong Kong Dept Mfg Engn & Engn Management Hong Kong Hong Kong Peoples R China

In this paper, an adaptive neural network (NN) control with a guaranteed L-infinity-gain performance is proposed for a class of parabolic partial differential equation (PDE) systems with unknown nonlinearities and persistent bounded disturbances. Initially, Galerkin method is applied to the PDE system to derive a low-order ordinary differential equation (ODE) system that accurately describes the dynamics of the dominant (slow) modes of the PDE system. Subsequently, based on the low-order slow model and the Lyapunov technique, an adaptive modal feedback controller is developed such that the closed-loop slow system is semiglobally input-to-state practically stable (ISpS) with an L-infinity-gain performance. In the proposed control scheme, a radial basis function (RBF) NN is employed to approximate the unknown term in the derivative of the Lyapunov function due to the unknown system nonlinearities. The outcome of the adaptive L-infinity-gain control problem is formulated as a linear matrix inequality (LMI) problem. Moreover, by using the existing LMI optimization technique, a suboptimal controller is obtained in the sense of minimizing an upper bound of the L-infinity-gain, while control constraints are respected. Furthermore, it is shown that the proposed controller can ensure the semiglobal input-to-state practical stability and L-infinity-gain performance of the closed-loop PDE system. Finally, by applying the developed design method to the temperature profile control of a catalytic rod, the achieved simulation results show the effectiveness of the proposed controller.

关键词： adaptive control distributed parameter systems input-to-state stability (ISS) linear matrix inequality (LMI) L-infinity-gain control neural network (NN)

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Synthesis of Equation-Free Control Structures for Dissipative distributed parameter systems Using Proper Orthogonal Decomposition and Discrete Empirical Interpolation Methods

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INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH 2017年第36期56卷 10110-10122页

作者： Yang, Manda Armaou, Antonios Penn State Univ Dept Chem Engn University Pk PA 16802 USA Wenzhou Univ Dept Mech Engn Wenzhou Zhejiang Peoples R China

We describe an equation-free control framework for the regulation of dissipative distributed parameter systems, with emphasis on improving the accuracy of the estimation by using a correction term. This control method is capable of regulating systems that have unknown dynamics but known effect of the control action. The system state and the dynamics are estimated by using the offline observations (snapshots ensemble) and the online continuous measurement of a restricted number of point sensors. First, we construct a reduced order model (ROM) with unknown terms using Galerkin/proper orthogonal decomposition (POD). Then the state of the ROM is estimated by a static observer with the information from the state sensors, and the mapping between the dynamics of the system and velocity sensors are generated using a similar approach. A discrete empirical interpolation method (DEIM) is employed to determine the sensor locations. To improve the accuracy of the estimation, a correction term is updated consistently. The proposed equation-free control framework is illustrated through a diffusion-reaction process and the performance of the proposed method is evaluated by simulation.

关键词： CHEMICAL structure SYNTHESIS (Chemistry) distributed parameter systems ORTHOGONAL decompositions INTERPOLATION ESTIMATION theory

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Backstepping-based sliding mode fault-tolerant control for linear interconnected parabolic distributed parameter systems

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IET CONTROL THEORY AND APPLICATIONS 2020年第14期14卷 1928-1936页

作者： Xu, Yongyuan Yang, Hao Jiang, Bin Cocquempot, Vincent Nanjing Univ Aeronaut & Astronaut Coll Automat Engn Nanjing Peoples R China Univ Lille Ctr Rech Informat Signal & Automat Lille Cent Lille CNRSUMR 9189 F-59000 Lille France

This study considers the fault-tolerant control (FTC) issue for a class of linear interconnected parabolic distributed parameter systems by utilising the backstepping-based sliding mode control technique. The original interconnected system, which suffers from process/actuator faults and matched disturbances, is converted into a stable target system by using an invertible backstepping transformation. Two types of kernel functions, the distinct diffusivity and the same diffusivity, are obtained. A sliding mode FTC scheme is developed to eliminate the destabilising effects caused by process/actuator faults and matched disturbances. An industrial application example is presented to validate the applicability and the relevance of the developed methodology.

关键词： nonlinear control systems control system synthesis control nonlinearities variable structure systems distributed parameter systems fault tolerance adaptive control actuators invertible backstepping transformation sliding mode FTC scheme matched disturbances mode fault-tolerant control fault-tolerant control issue linear interconnected parabolic distributed parameter systems backstepping-based mode control technique original interconnected system stable target system

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Using H₂-Control Performance Metrics for the Optimal Actuator Location of distributed parameter systems

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2015年第2期60卷 450-462页

作者： Morris, Kirsten Demetriou, Michael A. Yang, Steven D. Univ Waterloo Dept Appl Math Waterloo ON N2L 3G1 Canada Worcester Polytech Inst Dept Mech Engn Worcester MA 01609 USA Univ Waterloo Dept Elect & Comp Engn Waterloo ON N2L 3G1 Canada

This paper is concerned with the use of H-2-control performance metrics in finding optimal actuator locations for a class of infinite-dimensional systems. Conditions that guarantee convergence of the optimal actuator location for the finite-dimensional representation of the infinite-dimensional system to the optimal actuator location of the original infinite-dimensional system are provided. Minimizing an H-2-performance index, parameterized by the possible actuator locations and disturbance functions, leads to optimal locations that in addition to enhanced performance, also provide robustness with respect to the spatial distribution of disturbances. Numerical studies for a cantilever beam and a diffusion problem are used to demonstrate the effects of the spatial distribution of disturbances on the optimal actuator location. The effect of the diffusivity parameter on the best actuator locations is also considered.

关键词： distributed parameter systems H-2-control optimal actuator location spatial disturbances

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Guidance of Mobile Actuator-Plus-Sensor Networks for Improved Control and Estimation of distributed parameter systems

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2010年第7期55卷 1570-1584页

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

This paper presents an abstract framework for the optimization of actuating and sensing devices in distributed parameter systems. The optimization is performed on the repositioning of these devices throughout the spatial domain. It is assumed that a network of mobile sensing and actuating devices is available to obtain measurements from the spatially distributed process and dispense control signals to the spatially distributed process. By taking advantage of the properties that the spatial operator that governs the process dynamics possesses, namely symmetry, coercivity and boundedness, a scheme for the guidance of a mobile actuator-plus-sensor network is developed and used for the performance enhancement of the spatial process. The class of systems is governed by diffusion PDEs equipped with actuators having a boxcar spatial distribution and a collocated sensing device that provides the spatially averaged state measurement over the range of the actuating device. Using Lyapunov stability arguments, a stable guidance scheme is provided for each of the mobile agents. Due to the specific structure of the closed loop system operator with time-varying input and output operators, the same guidance schemes are applicable to the dual problem of mobile sensors employed for enhancing the state estimation problem. Both a centralized state estimator with mobile sensors and a network of consensus distributed estimators are considered, since both filters can be shown to result in the specific algebraic structure of a symmetric spatial operator with collocated input and output operators. Extensive numerical simulations for a 1-D diffusion equation with two actuator/sensor agents, a 2-D diffusion equation with one collocated actuator/sensor agent plus a centralized filter for a 1-D diffusion equation are included to verify the effectiveness of a such a mobile actuator-plus-sensor network in suppressing the effects of spatially varying disturbances and enhancing the system's perform

关键词： Centralized filters distributed consensus filters distributed parameter systems mobile actuators mobile sensors

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SLIDING MODE CONTROL OF distributed-parameter systems

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AUTOMATICA 1994年第12期30卷 1961-1966页

作者： LI, KC LEUNG, TP HU, YM S CHINA UNIV TECHNOL DEPT AUTOMATCANTON 510641PEOPLES R CHINA HONG KONG POLYTECH DEPT ELECTR ENGNKOWLOONHONG KONG HONG KONG POLYTECH DEPT MECH & MARINE ENGNKOWLOONHONG KONG

The sliding mode control problem for distributed parameter systems (DPS) is studied. Two mathematical description theorems of sliding modes are obtained using a novel analysis approach. The existence conditions of sliding modes are proposed for general DPS;and the sliding mode (SM) controllers are also designed straightforwardly for a class of DPS. An important feature of the theory is that the system is made insensitive to system uncertainties once the sliding manifold is reached.

关键词： distributed parameter systems SLIDING STATES VARIABLE STRUCTURE CONTROL SYNTHESIS METHODS ROBUSTNESS

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