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Nonlinearity Measures for distributed parameter and Descriptor systems

IFAC-PapersOnLine 2020年第2期53卷 7545-7550页

作者： Pedro Reyero-Santiago Carlos Ocampo-Martinez Rolf Findeisen Richard D. Braatz Automatic Control Department Universitat Politècnica de Catalunya Institut de Robòtica i Informàtica Industrial (CSIC-UPC) 08028 Barcelona Spain Institute for Automation Engineering (IFAT) Laboratory for Systems Theory and Automatic Control Otto-von-Guericke Universität Magdeburg 39106 Magdeburg Germany Massachusetts Institute of Technology Room E19-551 77 Massachusetts Avenue Cambridge MA 02139 USA

Control design and state estimation are usually more straightforward for linear than for nonlinear dynamical systems, which has motivated the development of methods for quantifying the extent of nonlinearity in dynamical systems. Although many well-defined methods have been proposed for systems described by ordinary differential equations, such methods are not as well explored for dynamical systems described by PDEs and descriptor systems that represent most chemical processes. This paper reviews, discusses, and compares methods for the definition and computation of nonlinearity measures. The measures are categorized in terms of open- vs. closed-loop control topologies, theoretical vs. numerically computed, state transformation dependency, input scaling dependency, linearization vs. optimized linear modeling vs. average linear modeling, applicability to unstable dynamical systems, and applicability to the right-hand side of the state equation or to input-output relationships. Then extensions of the nonlinearity measures are discussed for hybrid systems and those described by coupled differential, integral, and algebraic equations, often referred to as descriptor/singular systems.

关键词： nonlinear systems process control nonlinear measures descriptor systems distributed parameter systems

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A study on damping rates and boundary feedback control in distributed parameter vibrating systems

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2020年第2期488卷 124082-000页

作者： Wei, Chunqiu Li, Liangliang Wang, Fei Cao, Xiaomin Chen, Yining Yang, Jing Beijing Inst Technol Sch Math & Stat Beijing 102488 Peoples R China Sun Yat Sen Univ Sino French Inst Nucl Engn & Technol Zhuhai 519082 Peoples R China Shanxi Univ Sch Math Sci Taiyuan 030006 Shanxi Peoples R China Tianjin Univ Sch Elect & Informat Engn Tianjin 300072 Peoples R China North China Elect Power Univ Sch Control & Comp Engn Beijing 102206 Peoples R China

The study of damping rates for distributed and boundary feedback control systems is important in the design of control mechanisms for distributed parameter systems. Despite the fact that many papers have been published regarding the determination of spectra and also possibly the sharpest systemwide uniform rates of energy decay, many problems remain open. In this paper, we first mention a few examples of distributed and boundary damping, then proceed to examine the simplest such possible case of boundary feedback control of the one-dimensional wave equation. Using the wave propagation method, one can see that the analysis of the spectra is quite sophisticated. Indeed, for most cases, with seemingly the best efforts one can only pin down the rates of damping in some narrow range. Several open questions are posed at the end of the paper, which along with higher dimensional problems we hope will further motivate more studies in such decay spectral analysis. (C) 2020 Elsevier Inc. All rights reserved.

关键词： Damping rates Wave equation distributed and boundary feedback control distributed parameter systems

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Iterative learning control for one-dimensional fourth order distributed parameter systems

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Science China(Information Sciences) 2017年第1期60卷 177-189页

作者： Qin FU Panpan GU Jianrong WU School of Mathematics and Physics Suzhou University of Science and Technology

This paper addresses the problem of iterative learning control algorithm for high order distributed parameter systems in the presence of initial errors. And the considered distributed parameter systems are composed of the one-dimensional fourth order parabolic equations or the one-dimensional fourth order wave equations. According to the characteristics of the systems, iterative learning control laws are proposed for such fourth order distributed parameter systems based on the P-type learning scheme. When the learning scheme is applied to the systems, the output tracking errors on 2L space are bounded, and furthermore, the tracking errors on 2L space can tend to zero along the iteration axis in the absence of initial errors. Simulation examples illustrate the effectiveness of the proposed method.

关键词： P-type learning scheme iterative learning control distributed parameter systems fourth order parabolic equation fourth order wave equation

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Delay-Dependent Exponential Stabilization for Linear distributed parameter systems With Time-Varying Delay

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JOURNAL OF DYNAMIC systems MEASUREMENT AND CONTROL-TRANSACTIONS OF THE ASME 2018年第5期140卷 051003-051003页

作者： Wang, Jun-Wei Sun, Chang-Yin Univ Sci & Technol Beijing Sch Automat & Elect Engn Minist Educ Key Lab Knowledge Automat Ind Proc Beijing 100083 Peoples R China Southeast Univ Sch Automat Nanjing 210096 Jiangsu Peoples R China

This paper extends the framework of Lyapunov-Krasovskii functional to address the problem of exponential stabilization for a class of linear distributed parameter systems (DPSs) with continuous differentiable time-varying delay and spatiotemporal control input, where the system model is described by parabolic partial differential-difference equations (PDdEs) subject to homogeneous Neumann or Dirichlet boundary conditions. By constructing an appropriate Lyapunov-Krasovskii functional candidate and using some inequality techniques (e.g., spatial integral form of Jensen's inequalities and vector-valued Wirtinger's inequalities), some delay-dependent exponential stabilization conditions are derived, and presented in terms of standard linear matrix inequalities (LMIs). These stabilization conditions are applicable to both slow-varying and fast-varying time delay cases. The detailed and rigorous proof of the closed-loop exponential stability is also provided in this paper. Moreover, the main results of this paper are reduced to the constant time delay case and extended to the stochastic time-varying delay case, and also extended to address the problem of exponential stabilization for linear parabolic PDdE systems with temporal control input. The numerical simulation results of two examples show the effectiveness and merit of the main results.

关键词： exponential stabilization distributed parameter systems time-delay systems Jensen's inequality Wirtinger's inequality

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Improved control for distributed parameter systems with time-dependent spatial domains utilizing mobile sensor-actuator networks

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Chinese Physics B 2017年第9期26卷 7-16页

作者：张建中崔宝同庄波 Key Laboratory of Advanced Process Control for Light Industry(Ministry of Education)jiangnan University Wuxi 214122China

A guidance policy for controller performance enhancement utilizing mobile sensor-actuator networks （MSANs） is proposed for a class of distributed parameter systems （DPSs）, which are governed by diffusion partial differential equations （PDEs） with time-dependent spatial domains. Several sufficient conditions for controller performance enhancement are presented. First, the infinite dimensional operator theory is used to derive an abstract evolution equation of the systems under some rational assumptions on the operators, and a static output feedback controller is designed to control the spatial process. Then, based on Lyapunov stability arguments, guidance policies for collocated and non-collocated MSANs are provided to enhance the performance of the proposed controller, which show that the time-dependent characteristic of the spatial domains can significantly affect the design of the mobile scheme. Finally, a simulation example illustrates the effectiveness of the proposed policy.

关键词： distributed parameter systems time-dependent spatial domains mobile actuator-sensor networks,Lyapunov stability

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Fault Diagnosis of distributed parameter systems Modeled by Linear Parabolic Partial Differential Equations With State Faults

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JOURNAL OF DYNAMIC systems MEASUREMENT AND CONTROL-TRANSACTIONS OF THE ASME 2018年第1期140卷 011010-011010页

作者： Ferdowsi, Hasan Jagannathan, S. Texas A&M Univ Elect Engn Dept 7101 Univ Ave Texarkana TX 75503 USA Missouri Univ Sci & Technol Dept Elect & Comp Engn 301 West 16th St Rolla MO 65409 USA

In this paper, the problem, of fault diagnosis in distributed parameter systems (DPS) is investigated. The behavior of DPS is best described by partial differential equation (PDE) models. In contrast io transforming the DPS into a finite set of ordinary differential equations (ODE) prior to the design of control or fault detection schemes by using significant approximations, thus reducing the accuracy and reliability of the overall system, in this paper, the PDF representation of the system is directly utilized to construct a fault detection observer. A fault is detected by comparing the detection residual, which is the difference between measured and estimated outputs, with a predefined detection threshold. Once the fault is detected, an adaptive approximator is activated to learn the fault function. The estimated fault parameters are then compared with their failure thresholds to provide an estimate of the remaining useful life of the system. The scheme is verified in simulations on a heat system which is described by parabolic PDEs.

关键词： Simulation distributed parameter systems Approximation Failure Fault diagnosis Filters Flaw detection Partial differential equations Design Heat

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Improved control of distributed parameter systems using wireless sensor and actuator networks:An observer-based method

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Chinese Physics B 2017年第4期26卷 59-65页

作者：江正仙崔宝同楼旭阳庄波 School of Science Jiangnan UniversityWuxi 214122China School of loT Engineering Jiangnan UniversityWuxi 214122China Key Laboratory of Advanced Process Control for Light Industry(Ministry of Education) Jiangnan UniversityWuxi 214122China

In this paper,the control problem of distributed parameter systems is investigated by using wireless sensor and actuator networks with the observer-based ***,a centralized observer which makes use of the measurement information provided by the fixed sensors is designed to estimate the distributed parameter *** mobile agents,each of which is affixed with a controller and an actuator,can provide the observer-based control for the target *** using Lyapunov stability arguments,the stability for the estimation error system and distributed parameter control system is proved,meanwhile a guidance scheme for each mobile actuator is provided to improve the control performance.A numerical example is finally used to demonstrate the effectiveness and the advantages of the proposed approaches.

关键词： distributed parameter systems wireless sensor and actuator networks mobile actuator observer

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Mixed H₂/H_∞ fuzzy proportional-spatial integral control design for a class of nonlinear distributed parameter systems

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FUZZY SETS AND systems 2017年 306卷 26-47页

作者： Wang, Jun-Wei Wu, Huai-Ning Yu, Yao Sun, Chang-Yin Univ Sci & Technol Beijing Sch Automat & Elect Engn Beijing 100083 Peoples R China Beijing Univ Aeronaut & Astronaut Beihang Univ Sch Automat Sci & Elect Engn Sci & Technol Aircraft Control Lab Beijing 100191 Peoples R China

In this paper, a fuzzy feedback control design problem with a mixed H-2/H-infinity performance is addressed by using the distributed proportional-spatial integral (P-sI) control approach for a class of nonlinear distributed parameter systems represented by semi linear parabolic partial differential-integral equations (PDIEs). The objective of this paper is to develop a fuzzy distributed P-sI controller with a mixed H-2/H-infinity performance index for the semi-linear parabolic PDIE system. To do this, the semi-linear parabolic PDIE system is first assumed to be exactly represented by a Takagi-Sugeno (T-S) fuzzy parabolic PDIE model in a given local domain of Hilbert space. Then, based on the T-S fuzzy PDIE model, a distributed fuzzy P-sI state feedback controller is proposed such that the closed-loop PDIE system is locally exponentially stable with a mixed H-2/H-infinity performance. The sufficient condition on the existence of the fuzzy controller is given by using the Lyapunov's direct method, the technique of integration by parts, and vector-valued Wirtinger's inequalities, and presented in terms of standard linear matrix inequalities (LMIs). Moreover, by using the existing LMI optimization techniques, a suboptimal H-infinity fuzzy controller is derived in the sense of minimizing an upper bound of a given H-2 performance function. Finally, the developed design methodology is successfully applied to feedback control of a semi-linear reaction diffusion system with spatial integral terms. (C) 2016 Elsevier B.V. All rights reserved.

关键词： distributed parameter systems Exponential stability Proportional-spatial integral control Takagi-Sugeno (T-S) fuzzy model Linear matrix inequalities (LMIs)

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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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Nonlinear observer for distributed parameter systems described by decoupled advection equations

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JOURNAL OF VIBRATION AND CONTROL 2017年第7期23卷 1152-1165页

作者： Kamran, Niloofar N. Drakunov, Sergey V. Solano, Wanda M. Embry Riddle Aeronaut Univ Dept Phys Sci 600 South Clyde Morris Blvd Daytona Beach FL 32114 USA

In this paper a nonlinear observer for a class of partial differential equations known as the advection equation is designed. The observer, that uses only boundary measurements, is developed based on the sliding mode method. The convergence of states of the observer to the actual system, in spite of possible mismatches between the model and the system, is proven through the Lyapunov stability techniques. In addition, a sliding mode method is employed to design an anomaly detection system that is able to identify parameters of the disturbance in the system such as intensity and location. The Lyapunov stability theorem has been used in order to guarantee the convergence of the anomaly detection system. The applications of observer and anomaly detector are illustrated through simulation.

关键词： Nonlinear observers distributed parameter systems advection equation sliding mode variable structure systems method of characteristics anomaly detection fluid flow in pipes leakage detection

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