In this paper, two methods are reviewed and compared for designing reduced order controllers for distributed parameter systems. The first involves a reduction method known as LQG balanced truncation followed by MinMax...
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In this paper, two methods are reviewed and compared for designing reduced order controllers for distributed parameter systems. The first involves a reduction method known as LQG balanced truncation followed by MinMax control design and relies on the theory and properties of the distributedparameter system. The second is a neural network based adaptive output feedback synthesis approach, designed for the large scale discretized system and depends upon the relative degree of the regulated outputs. Both methods are applied to a problem concerning control of vibrations in a nonlinear structure with a bounded disturbance. (c) 2006 Elsevier Ltd. All rights reserved.
The modeling and control issues for distributed parameter systems (DPSs) have received a great deal of attention. Because linear model order reduction (MOR) methods may ignore the nonlinear dynamics and lose some deta...
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The modeling and control issues for distributed parameter systems (DPSs) have received a great deal of attention. Because linear model order reduction (MOR) methods may ignore the nonlinear dynamics and lose some details, it is difficult to describe DPS accurately by common modeling methods. To effectively model such systems, a sparse stacked auto-encoder and gated recurrent unit (SSAE-GRU) model is proposed in this paper. Under the time/space separation theory, it is the mainstream way to perform MOR and identification of time series respectively. In the SSAE-GRU model, this practice is still adhered to but joint learning is recommended. SSAE can be used as an excellent MOR technique. A sparse activation strategy that is introduced makes its model space simple and easy to train. GRU has the ability to represent such complex temporal properties because the information stored by previous neurons can be transmitted to the current moment selectively. The joint training method allows them to be responsible and consider the connection between adjacent moments and spatial energy transfer overall. Then, we use L2 regularization in back-propagation to reduce the difficulty of model optimization and prevent overfitting. The modeling scheme is simulated on two typical chemical thermal processes. This article demonstrates the effectiveness of the proposed method as well as outstanding performance compared to existing methods.
This article is concerned with the controller design for distributed parameter systems with time delays in the boundary. An implementable control law is presented in light of a state predictor, and a feasible calculat...
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This article is concerned with the controller design for distributed parameter systems with time delays in the boundary. An implementable control law is presented in light of a state predictor, and a feasible calculation scheme of this control law is provided based on the adjoint theory. The resulting closed-loop system is proved to be exponentially stable. As an application, a one-dimensional Schrodinger equation with a delay input is introduced and the numerical simulation verifies the feasibility of the suggested control law.
A new method to approximate distributed parameter systems, which normally have an infinite dimension, by finite dimensional linear systems is presented. The impulse and step responses of the original systems are well ...
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A new method to approximate distributed parameter systems, which normally have an infinite dimension, by finite dimensional linear systems is presented. The impulse and step responses of the original systems are well approximated by using the singular value decomposition. A telegraph cable example is presented to demonstrate the usefulness of the method.
In this contribution we address the issue of estimating parameters of a process, which is described by a set of first order, quasi-linear partial differential equations (PDEs) from a set of measurements. The parameter...
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In this contribution we address the issue of estimating parameters of a process, which is described by a set of first order, quasi-linear partial differential equations (PDEs) from a set of measurements. The parameters are found by minimizing the sum of the square of the errors over a finite set of measurement data. The errors are defined as the differences between the model Outputs and corresponding measurements. Since the assumption of constant model parameters may not be realistic in many practical applications, the estimation is carried out using a moving and fixed-size window of data. When a new measurement becomes available, the oldest measurement is discarded and the new one is added. (C) 2009 Elsevier Ltd. All rights reserved.
In this paper we consider the stabilization of continuous-time distributed parameter systems by piecewise polynomial controls, We obtain necessary and sufficient conditions for stabilization by piecewise polynomial co...
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In this paper we consider the stabilization of continuous-time distributed parameter systems by piecewise polynomial controls, We obtain necessary and sufficient conditions for stabilization by piecewise polynomial controls.
The least mean squared error linear one-stage predictor and filter are derived for discrete-time distributed parameter systems with uncertain observations. The measurements are taken at several fixed points of the spa...
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The least mean squared error linear one-stage predictor and filter are derived for discrete-time distributed parameter systems with uncertain observations. The measurements are taken at several fixed points of the spatial domain. We have used an orthogonal projection approach. (C) 1998 John Wiley & Sons, Ltd.
We consider a class of second-order distributed parameter systems with structured perturbations in which both partial position and partial velocity measurements are assumed available. The control objective is to desig...
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We consider a class of second-order distributed parameter systems with structured perturbations in which both partial position and partial velocity measurements are assumed available. The control objective is to design an adaptive controller so that the plant state follows the state of a second-order reference model despite the presence of the perturbation terms. Copyright (C) 2006 John Wiley & Sons, Ltd.
AbstractIn controlling distributed parameter systems it is often desirable to obtain low‐order, finite‐dimensional controllers in order to minimize real‐time computational requirements. Standard approaches to this ...
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AbstractIn controlling distributed parameter systems it is often desirable to obtain low‐order, finite‐dimensional controllers in order to minimize real‐time computational requirements. Standard approaches to this problem employ model/controller reduction techniques in conjunction with LQG theory. In this paper we consider the finite‐dimensional approximation of the infinite‐dimensional Bernstein/Hyland optimal projection theory. Our approach yields fixed‐finite‐order controllers which are optimal with respect to high‐order, approximating, finite‐dimensional plant models. We illustrate the technique by computing a sequence of first‐order controllers for one‐dimensional, single‐input/single‐output parabolic (heat/diffusion) and hereditary systems using a spline‐based, Ritz‐Galerkin, finite element approximation. Our numerical studies indicate convergence of the feedback gains with less than 2% performance degradation over full‐order LQG controllers for the parabolic system and 10% degrad
This paper introduces a fuzzy control (FC) under spatially local averaged measurements (SLAMs) for nonlinear-delayed distributed parameter systems (DDPSs) represented by parabolic partial differential-difference equat...
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This paper introduces a fuzzy control (FC) under spatially local averaged measurements (SLAMs) for nonlinear-delayed distributed parameter systems (DDPSs) represented by parabolic partial differential-difference equations (PDdEs), where the fast-varying time delay and slow-varying one are considered. A Takagi-Sugeno (T-S) fuzzy PDdE model is first derived to exactly describe the nonlinear DDPSs. Then, by virtue of the T-S fuzzy PDdE model and a Lyapunov-Krasovskii functional, an FC design under SLAMs, where the membership functions of the proposed FC law are determined by the measurement output and independent of the fuzzy PDdE plant model, is developed on basis of spatial linear matrix inequalities (SLMIs) to guarantee the exponential stability for the resulting closed-loop DDPSs. Lastly, a numerical example is offered to support the presented approach.
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