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A spatial domain decomposition approach to distributed H _∞ observer design of a linear unstable parabolic distributed parameter system with spatially discrete sensors

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INTERNATIONAL JOURNAL OF CONTROL 2017年第12期90卷 2772-2785页

作者： Wang, Jun-Wei Liu, Ya-Qiang Hu, Yan-Yan Sun, Chang-Yin Univ Sci & Technol Beijing Sch Automat & Elect Engn Beijing Peoples R China

This paper discusses the design problem of distributed H-infinity Luenberger-type partial differential equation (PDE) observer for state estimation of a linear unstable parabolic distributed parameter system (DPS) with external disturbance and measurement disturbance. Both pointwise measurement in space and local piecewise uniform measurement in space are considered;that is, sensors are only active at some specified points or applied at part thereof of the spatial domain. The spatial domain is decomposed into multiple subdomains according to the location of the sensors such that only one sensor is located at each subdomain. By using Lyapunov technique, Wirtinger's inequality at each subdomain, and integration by parts, a Lyapunov-based design of Luenberger-type PDE observer is developed such that the resulting estimation error system is exponentially stable with an H-infinity performance constraint, and presented in terms of standard linear matrix inequalities (LMIs). For the case of local piecewise uniform measurement in space, the first mean value theorem for integrals is utilised in the observer design development. Moreover, the problem of optimal H-infinity observer design is also addressed in the sense of minimising the attenuation level. Numerical simulation results are presented to show the satisfactory performance of the proposed design method.

关键词： State estimation Luenberger-type observer spatially discrete sensors distributed parameter system linear matrix inequality (LMI)

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Robust stabilization of the distributed parameter system with time delay via fuzzy control

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IEEE TRANSACTIONS ON FUZZY systemS 2008年第3期16卷 567-584页

作者： Yuan, Kun Li, Han-Xiong Cao, Jinde Southeast Univ Dept Math Nanjing 210096 Peoples R China Southeast Univ Sch Automat Nanjing 210096 Peoples R China City Univ Hong Kong Dept Mfg Engn & Engn Management Hong Kong Hong Kong Peoples R China

In this paper, stabilization of the distributed parameter system (DPS) with time delay is studied using Galerkin's method and fuzzy control. With the help of Galerkin's method, the dynamics of DPS with time delay can be first converted into a group of low-order functional ordinary differential equations, which will be used for design of the robust fuzzy controller. The fuzzy controller designed can guarantee exponential stability of the closed-loop DPS. Some sufficient conditions are derived for the stabilization together with the linear matrix inequality design approach. The effectiveness of the proposed control design methodology is demonstrated in numerical simulations.

关键词： distributed parameter system exponential stability fuzzy control Galerkin's method linear matrix inequality

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Partial synchronization of the distributed parameter system with time delay via fuzzy control

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IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION 2014年第1期31卷 51-72页

作者： Yuan, Kun Fei, Shumin Cao, Jinde Southeast Univ Sch Automat Nanjing 210096 Jiangsu Peoples R China Southeast Univ Dept Math Nanjing 210096 Jiangsu Peoples R China

In this paper, partial synchronization of the distributed parameter system (DPS) with time delay is considered via Galerkin's method and the fuzzy control. First, based on Galerkin's method, the dynamics of master DPS and slave DPS can be described by low-order ordinary differential equations (ODEs). Then the low-order functional ODEs are used as the basis for the design of the fuzzy controller to ensure the synchronization between the two low-order ODEs;moreover, when the slow system of master DPS and the slow system of slave DPS are synchronized, the error between master DPS and slave DPS is bounded. Some criteria are derived for stabilization and linear matrix inequality design approach is developed. The effectiveness of the proposed controller design methodology is finally demonstrated through numerical simulation.

关键词： distributed parameter system partial synchronization Galerkin's method fuzzy control linear matrix inequality

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2D Inverse Problem in a distributed parameter system

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INTERNATIONAL JOURNAL OF CONTROL AUTOMATION AND systemS 2013年第6期11卷 1106-1111页

作者： Rachidi, Said Channa, Rafik Karama, Asma Fac Sci Semlalia Automat Lab Dept Phys Marrakech 40000 Morocco

In this paper, we present a numerical solution for an inverse heat problem to estimate 2D space-wise coefficient in a parabolic system describing heat transfer. The inverse problem is recast into an optimization problem solved with a conjugate gradient method. This approach use the non linear optimization formulation by minimizing a cost function taking into account both the measured outputs of the system and the outputs calculated by means of the model. The solution is performed by using the free finite element software FreeFem. Numerical example is carried out to check the validity of the proposed method.

关键词： distributed parameter system identification inverse problem minimization

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Dynamic switching based fuzzy control strategy for a class of distributed parameter system

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JOURNAL OF PROCESS CONTROL 2014年第3期24卷 88-97页

作者： Ren, Yao-Qing Duan, Xiao-Gang Li, Han-Xiong Chen, C. L. Philip Cent South Univ State Key Lab High Performance Complex Mfg Changsha 410083 Hunan Peoples R China City Univ Hong Kong Dept Syst Engn & Engn Management Hong Kong Hong Kong Peoples R China Univ Macau Fac Sci & Technol Macau Peoples R China

In this work, a dynamic switching based fuzzy controller combined with spectral method is proposed to control a class of nonlinear distributed parameter systems (DPSs). Spectral method can transform infinite-dimensional DPS into finite ordinary differential equations (ODEs). A dynamic switching based fuzzy controller is constructed to track reference values for the multi-inputs multi-outputs (MIMO) ODEs. Only a traditional fuzzy logic system (FLS) and a rule base are used in the controller, and membership functions (MFs) for different ODEs are adjusted by scaling factors. Analytical models of the dynamic switching based fuzzy controller are deduced to design the scaling factors and analyze stability of the control system. In order to obtain a good control performance, particle swarm optimization (PSO) is adopted to design the scaling factors. Moreover, stability of fuzzy control system is analyzed by using the analytical models, definition of the stability and Lyapunov stability theory. Finally, a nonlinear rod catalytic reaction process is used as an illustrated example for demonstration. The simulation results show that performance of proposed dynamic switching based fuzzy control strategy is better than a multi-variable fuzzy logic controller. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： distributed parameter system Particle swarm optimization Dynamic switching Fuzzy logic controller Spectral method

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parameter identification for a parabolic distributed parameter system using the finite integral transform technique

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JOURNAL OF CHEMICAL ENGINEERING OF JAPAN 1996年第2期29卷 386-389页

作者： Yoshida, M Hanutsaha, R Matsumoto, S 1) Depatment of Chem. Eng. Tohoku Univ.

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Missing Output Identification Model Based Recursive Least Squares Algorithm for a distributed parameter system

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INTERNATIONAL JOURNAL OF CONTROL AUTOMATION AND systemS 2018年第1期16卷 150-157页

作者： Chen, Jing Jiang, Bin Li, Juan Nanjing Univ Aeronaut & Astronaut Coll Automat Engn Nanjing 210016 Jiangsu Peoples R China Qingdao Agr Univ Coll Mech & Elect Engn Qingdao 266109 Peoples R China

This paper proposes a recursive least squares algorithm for a distributed parameter system with missing observations. By using the finite difference method, the distributed parameter system can be turned into a lumped parameter system. Then a missing output identification model based recursive least squares algorithm is derived to estimate the unknown parameters of the lumped parameter system. Furthermore, the parameters of the distributed parameter system can be computed by the estimated parameters of the lumped parameter system. The simulation results indicate that the proposed method is effective.

关键词： distributed parameter system finite difference method missing output identification model parameter estimation recursive least squares

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Application of reduced models for robust control and state estimation of a distributed parameter system

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JOURNAL OF PROCESS CONTROL 2009年第3期19卷 539-549页

作者： Ding, Limei Johansson, Andreas Gustafsson, Thomas Lulea Univ Technol Div Syst & Interact SE-97187 Lulea Sweden

This paper studies the application of reduced models of a distributed parameter system for robust process control and state estimation. We take the approach of integrating model reduction, parameter identification, and model uncertainty analysis, in purpose to find an appropriate trade-off between complexity and robust performance. The application example is the temperature system in a continuous paper pulp digester. Physical modeling of this process results in coupled linearized partial differential equations which are then reduced into low-order nominal process models using an orthogonal collocation approximation method. Two different approaches to obtaining it model uncertainty description are adapted for use on a distributed parameter system with low-order nominal model and shown to produce similar results when tested with measurement data. It is also demonstrated how this uncertainty description, in combination with the reduced model, may be used for robust control design and verification of the control performance on the distributed parameter system. Finally, the possibility of estimating the distributed process state using a state observer for the reduced process is demonstrated. Measurements of the process state in a certain position is available and is shown to agree with the estimated state at the same position. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： distributed parameter system Reduced models Model uncertainty Paper pulp digester Robust control State estimation

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Mobile observation for distributed parameter system with moving boundary over mobile sensor networks

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Journal of Control and Decision 2021年第2期8卷 124-134页

作者： Jianzhong Zhang Baotong Cui Key Laboratory of Advanced Process Control for Light Industry(Ministry of Education) Jiangnan UniversityWuxiPeople’s Republic of China School of Internet of Things Engineering Jiangnan UniversityWuxi 214122People’s Republic of China School of Mathematics and Statistics Taishan UniversityTaian 271000People’s Republic of China

This paper considers the state observation for a class of distributed parameter systems(DPSs)with moving boundaries modelled by parabolic partial differential equations(PDEs).The method of mobile observation is presented to improve the observation performance of the systems and to eliminate the influence of moving boundaries on system observation with the aids of mobile sensor networks(MSNs).The MSNs which can move throughout the time-dependent spatial domain are used to provide the spatially averaged observations of the *** using the abstract evolution equation theory of parabolic PDEs and the Lyapunov stability arguments,a centralised observer is designed and a mobile control scheme for each of the mobile sensors is presented while taking account of the dynamics of the MSNs.A numerical example is finally presented to illustrate the effectiveness and the advantages of the proposed approach.

关键词： distributed parameter system moving boundary abstract evolution equation state observation mobile sensor network

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The Optimization of Controller Allocation by using Genetic Algorithms for Fuzzy Control of distributed parameter system

Denki Gakkai Ronbunshi. C, Erekutoronikusu Joho Kogaku, Shis...

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Denki Gakkai Ronbunshi. C, Erekutoronikusu Joho Kogaku, Shisutemu 1997年第7期117卷 979-979页

作者： Qi, T. Hiramatsu, T. Miyazaki, M. Keio University Kanto Gakuin University

The control of the distributed parameter system(DPS) has some problems like as that 1)the construction of the mathematical model of the DPS is difficult and 2) the allocation of control equipments must be optimized. For the former problem, we applied the fuzzy technique to the control of the DPS because it has dominance of that one can construct the control system with the experience rules but without the mathematical model. For the latter problem, the genetic algorithm(GA) was used because one can optimize the controller allocation with low calculation time by using it. Simulation experiments were performed for the temperature control problem on a finite length stick. As the result, effectiveness of the proposed method was confirmed.

关键词： distributed parameter system Fuzzy Control Technique Genetic Algorithms(GA)

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