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DC-boundary finite-time stabilisation for distributed parameter systems

IET CONTROL THEORY AND APPLICATIONS 2020年第15期14卷 2186-2196页

作者： Li, Manna Mao, Weijie Zhejiang Univ Inst Cyber Syst & Control Hangzhou 310027 Peoples R China

In this study, the finite-time stabilisation problem of distributed parameter systems with control acting on a Dirichlet condition (DC) boundary is considered. First, the corresponding distributed parameter system with inhomogeneous DC-boundaries is equivalently transformed into another distributed parameter system with homogeneous DC-boundaries. A DC-boundary feedback controller is then designed in terms of the distributed state, and sufficient conditions for L-2 finite-time stabilisation and W-1,W- 2 finite-time stabilisation of distributed parameter systems are provided through the use of Lyapunov functionals. The issues regarding the finite-time stabilisation of distributed parameter systems are converted into the feasibility of matrix inequalities, and the availability of the proposed results is verified through two numerical simulations.

关键词： Lyapunov methods control system synthesis feedback distributed parameter systems stability matrix algebra DC-boundary feedback controller DC-boundary finite-time stabilisation Dirichlet condition boundary distributed parameter system matrix inequalities Lyapunov functionals sufficient conditions numerical simulations

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ON THE OPTIMAL TUNING OF A ROBUST CONTROLLER FOR PARABOLIC distributed parameter-systems

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AUTOMATICA 1987年第6期23卷 719-728页

作者： POHJOLAINEN, S Tampere University of Technology Department of Mathematics SF-33101 Tampere 10 P.O. Box 527 Finland

Optimal tuning of robust multivariable controllers for stable parabolic distributed parameter systems is discussed. In order to evaluate the behaviour of the closed loop system, a quadratic criterion is selected. Then it is proved that the system may be decomposed into slow and fast subsystems, and that the value of the criterion will mainly depend on the slow subsystem. Tuning of the controller, for this subsystem, turns out to be a standard finite-dimensional quadratic regulator problem. Two examples are given to show the improvement due to the new selection of the control parameters.

关键词： Control theory distributed parameter systems linear optimal regulator multivariable systems PID-control robustness state-space methods

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A model-based fault detection and diagnosis scheme for distributed parameter systems: A learning systems approach

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ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS 2002年第3期7卷 43-67页

作者： Demetriou, MA Worcester Polytech Inst Dept Mech Engn Worcester MA 01609 USA Ctr Res Sci Computat Raleigh NC USA

In this note, fault detection techniques based on finite dimensional results are extended and applied to a class of infinite dimensional dynamical systems. This special class of systems assumes linear plant dynamics having an abrupt additive perturbation as the fault. This fault is assumed to be linear in the (unknown) constant (and possibly functional) parameters. An observer-based model estimate is proposed which serves to monitor the system's dynamics for unanticipated failures, and its well posedness is summarized. Using a Lyapunov synthesis approach extended and applied to infinite dimensional systems, a stable adaptive fault diagnosis (fault parameter learning) scheme is developed. The resulting parameter adaptation rule is able to "sense" the instance of the fault occurrence. In addition, it identifies the fault parameters using the additional assumption of persistence of excitation. Extension of the adaptive monitoring scheme to incipient faults (time varying faults) is summarized. Simulations studies are used to illustrate the applicability of the theoretical results.

关键词： fault detection distributed parameter systems

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Robust dissipative control for semilinear Markovian jump distributed parameter systems with time-varying delay and incomplete transition probabilities

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ASIAN JOURNAL OF CONTROL 2020年第6期22卷 2513-2526页

作者： Song, Xiaona Wang, Mi Song, Shuai Lu, Junwei Man, Jingtao Henan Univ Sci & Technol Sch Informat Engn Luoyang 471023 Peoples R China Nanjing Univ Sci & Technol Sch Automat Nanjing Jiangsu Peoples R China Nanjing Normal Univ Sch Elect & Automat Engn Nanjing Jiangsu Peoples R China

This paper investigates the robust stabilization problem of semilinear Markovian jump distributed parameter systems (which are modeled by parabolic partial differential equations) with time-varying delay and incomplete transition probabilities. Based on Takagi-Sugeno (T-S) fuzzy theory, a T-S fuzzy model is obtained to describe the nonlinear systems. Furthermore, by constructing a novel Lyapunov functional candidate, several sufficient delay-dependent conditions, which ensure the considered systems stochastically stable and strictly dissipative, are established in terms of linear matrix inequalities. Finally, a fuzzy controller design approach is proposed, and two examples are presented to demonstrate the effectiveness of the designed controller.

关键词： distributed parameter systems incomplete transition probabilities Markovian jump systems Robust dissipative control time-varying delay

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Engineering Methods and Software Support for Modeling and Design of Discrete-time Control of distributed parameter systems

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EUROPEAN JOURNAL OF CONTROL 2009年第3-4期15卷 407-417页

作者： Hulko, G. Belavy, C. Meszaros, A. Bucek, P. Ondrejkovic, K. Zajicek, P. Fac Mech Engn Inst Automat Measurement & Appl Informat Bratislava 81231 Slovakia Fac Chem & Food Technol Inst Informat Engn Automat & Math Bratislava 81237 Slovakia Slovak Tech Univ Bratislava Kosice Slovakia

In this mini-tutorial some advanced engineering methods are presented for modeling and design of discrete-time control of distributed parameter systems described fir control purposes by numerical structures over complex-shape 3D definition domains along with the software package distributed parameter systems Blockset for MATLAB & Simulink - Third-Party Math Works product, inspired by the boom of numerical analysis of dynamics of machines and processes within engineering practice. The techniques offered are completed by a user-friendly web service tool, suitable for interactive solution of model control problems of distributed parameter systems via the Internet.

关键词： distributed parameter systems Discrete-time control Engineering methods Software support

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H_∞ sampled-data fuzzy control for non-linear parabolic distributed parameter systems with control inputs missing

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IET CONTROL THEORY AND APPLICATIONS 2017年第10期11卷 1530-1541页

作者： Wang, Zi-Peng Wu, Huai-Ning Univ Jinan Sch Elect Engn Jinan 250022 Peoples R China Beihang Univ Sch Automat Sci & Elect Engn Sci & Technol Aircraft Control Lab Beijing 100191 Peoples R China

In this study, an sampled-data fuzzy control problem is considered for non-linear parabolic partial differential equation (PPDE) systems with control inputs missing. It is assumed that the actuator to the plant is set to zero if the control inputs missing which occurs in a random way satisfies a Bernoulli distribution. With the aid of the modal decomposition technique, a non-linear ordinary differential equation (ODE) system is initially obtained to represent the dominant dynamics of the PPDE system. Subsequently, a Takagi-Sugeno fuzzy model is utilised to accurately describe the resulting non-linear ODE system. Then, using a novel time-dependent functional and the stochastic analysis technique, an sampled-data fuzzy controller with the stochastic missing data via linear matrix inequalities is proposed to stabilise exponentially the non-linear PPDE system in the mean square sense and achieve an performance for the derived non-linear ODE system. Finally, an example on a temperature cooling fin is given to verify the proposed design strategy.

关键词： H control sampled data systems fuzzy control nonlinear control systems distributed parameter systems partial differential equations nonlinear differential equations linear matrix inequalities asymptotic stability stochastic systems H sampled-data fuzzy control nonlinear parabolic distributed parameter systems control input missing nonlinear parabolic partial differential equation systems PPDE system Bernoulli distribution modal decomposition technique nonlinear ordinary differential equation system nonlinear ODE system Takagi-Sugeno fuzzy model time-dependent functional stochastic analysis technique stochastic missing data linear matrix inequalities temperature cooling fin actuator exponential stability

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DNN-state identification of 2D distributed parameter systems

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INTERNATIONAL JOURNAL OF systems SCIENCE 2012年第2期43卷 296-307页

作者： Chairez, I. Fuentes, R. Poznyak, A. Poznyak, T. Escudero, M. Viana, L. IPN UPIBI Dept Bioelect Mexico City 07738 DF Mexico IPN CINVESTAV Dept Automat Control Mexico City 07738 DF Mexico IPN ESIQIE SEPI Mexico City 07738 DF Mexico

There are many examples in science and engineering which are reduced to a set of partial differential equations (PDEs) through a process of mathematical modelling. Nevertheless there exist many sources of uncertainties around the aforementioned mathematical representation. Moreover, to find exact solutions of those PDEs is not a trivial task especially if the PDE is described in two or more dimensions. It is well known that neural networks can approximate a large set of continuous functions defined on a compact set to an arbitrary accuracy. In this article, a strategy based on the differential neural network (DNN) for the non-parametric identification of a mathematical model described by a class of two-dimensional (2D) PDEs is proposed. The adaptive laws for weights ensure the 'practical stability' of the DNN-trajectories to the parabolic 2D-PDE states. To verify the qualitative behaviour of the suggested methodology, here a non-parametric modelling problem for a distributed parameter plant is analysed.

关键词： neural networks adaptive identification distributed parameter systems partial differential equations practical stability

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Feedback control of hyperbolic distributed parameter systems

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CHEMICAL ENGINEERING SCIENCE 2005年第4期60卷 969-980页

作者： Shang, HL Forbes, JF Guay, M Laurentian Univ Sch Engn Sudbury ON P3E 2C6 Canada Univ Alberta Dept Chem & Mat Engn Edmonton AB T6G 2G6 Canada Queens Univ Dept Chem Engn Kingston ON K7L 3N6 Canada

Hyperbolic distributed parameter systems (DPS) represent a large number of industrial processes with spatially nonuniform operating variable profiles. Research has been conducted to develop high-performance control strategies for these systems by exploiting their high-fidelity models. In this paper, a feedback control method that yields improved performance is proposed for DPS modelled by first-order hyperbolic partial differential equations (PDEs) using the method of characteristics. Simulation results show that this method can provide effective control for the systems modelled by a scalar PDE as well as a system of PDEs. Further, it can efficiently compensate the effect of model-plant mismatch and effectively reject the disturbances. (C) 2004 Published by Elsevier Ltd.

关键词： feedback control distributed parameter systems method of characteristics hyperbolic PDE process control

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NON-LINEAR STATE ESTIMATION AND FEEDBACK-CONTROL OF NON-LINEAR AND BILINEAR distributed parameter-systems

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JOURNAL OF DYNAMIC systems MEASUREMENT AND CONTROL-TRANSACTIONS OF THE ASME 1981年第2期103卷 78-83页

作者： BALAS, MJ Electrical and Systems Engineering Department Rensselaer Polytechnic Institute Troy N.Y. 12181

This paper presents a theory of nonlinear state observers for nonlinear and bilinear distributed parameter systems. Convergence results are proved for these observers. Linear feedback control derived from such state observers is applied to the distributed parameter system and conditions are presented for closed-loop stability. The emphasis is on finite dimensional state observers and controllers (which can be implemented with on-line computers) and conditions for their successful operation with infinite dimensional distributed parameter systems.

关键词： Stability State estimation Computers distributed parameter systems Control equipment Feedback

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Model-based fault detection, estimation, and prediction for a class of linear distributed parameter systems

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AUTOMATICA 2016年 66卷 122-131页

作者： Cai, Jia Ferdowsi, Hasan Sarangapani, Jagannathan Missouri Univ Sci & Technol Dept Elect & Comp Engn Rolla MO 65409 USA

This paper addresses a new model-based fault detection, estimation, and prediction scheme for linear distributed parameter systems (DPSs) described by a class of partial differential equations (PDEs). An observer is proposed by using the PDE representation and the detection residual is generated by taking the difference between the observer and the physical system outputs. A fault is detected by comparing the residual to a predefined threshold. Subsequently, the fault function is estimated, and its parameters are tuned via a novel update law. Though state measurements are utilized initially in the parameter update law for the fault function estimation, the output and input filters in the modified observer subsequently relax this requirement. The actuator and sensor fault functions are estimated and the time to failure (TTF) is calculated with output measurements alone. Finally, the performance of detection, estimation and a prediction scheme is evaluated on a heat transfer reactor with sensor and actuator faults. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Fault detection Fault estimation Fault prognosis Partial differential equations distributed parameter systems

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