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Application of Decomposition/Coordination Methods to Control and Identification of Interconnected distributed-parameter systems

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IFAC Proceedings Volumes 1983年第10期16卷 539-544页

作者： A. Munack M. Thoma Institut für Regelungstechnik Universität Hannover Appelstrasse 11 D 3000 Hannover 1 Federal Republic of Germany

Application of two decomposition/coordination methods to interconnected distributed-parameter systems of parabolic type is treated. After formulation of both methods - penalization and re-injection - for the optimal control problem, the methods are also formulated for resolution of the parameter identification problem. An emphasis lies in the treatment of parameters that occur in several subproblems simultaneously. From computational experiences it can be stated, that decomposition/coordination methods applied to parameter identification work highly satisfactory and are much less time-consuming than the treatment of the corresponding coupled equations. A simple example is given at the end of the paper.

关键词： distributed-parameter systems large-scale systems decomposition techniques optimal control identification

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ɛ-Coupling and Singular Perturbation Approaches to the Control of Interconnected distributed parameter systems

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IFAC Proceedings Volumes 1983年第10期16卷 251-258页

作者： S.G. Tzafestas Control Systems Laboratory University of Patras Patras Greece

Many distributed-parameter systems consist of interconnected subsystems involving fast and slow physical phenomena or reducing to a number of independent subsystems when a scalar parameter ε is zero. The purpose of this paper is to treat the optimal control of such systems by invoking the ε-coupling and singular perturbation approaches developed by Kokotovic and his associates for lumped-parameter large-scale systems. In the case of ε-coupled distributed-parameter systems it is shown that the optimal state feedback matrix can be approximated by a Volterra-MacLaurin series with coefficients determined by solving two lower-order decoupled Riccati and linear equations. By using an mth-order approximation of the optimal feedback matrix, one obtains a (2m+l)th order approximation of the optimal performance function. In the singular perturbation approach the result is that for an O(ε 2 ) suboptimal control one must solve two decoupled Riccati equations, one for the fast and one for the slow subsystem and then construct appropriately the composite control law. By using only the Riccati equation for the slow subsystem, one obtains an 0(ε) suboptimal control. The singular perturbation technique can also be used to treat interconnected distributed-parameter systems involving many strongly coupled slow subsystems and weakly coupled fast subsystems.

关键词： ε-coupling method singular perturbations interconnected systems distributed-parameter systems large scale systems slow and fast control

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NECESSARY AND SUFFICIENT CONDITIONS FOR OPTIMAL-CONTROL OF QUASILINEAR PARTIAL-DIFFERENTIAL systems

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1984年第1期43卷 89-101页

作者： DERZKO, NA SETHI, SP THOMPSON, GL UNIV TORONTO FAC MANAGEMENT SCITORONTO M5S 1A1ONTARIOCANADA CARNEGIE MELLON UNIV GRAD SCH IND ADMPITTSBURGHPA 15213

First-order necessary and sufficient conditions are obtained for the following quasilinear distributed-parameter optimal control problem:$$max\left\{ {J(u) = \int_\Omega {F(x,u,t) d\omega + } \int_{\partial \Omega } {G(x,t) \cdot d\sigma } } \right\},$$ subject to the partial differential equation$$A(t)x = f(x,u,t),$$ wheret,u,G are vectors andx,F are scalars. Use is made of then-dimensional Green's theorem and the adjoint problem of the equation. The second integral in the objective function is a generalized surface integral. Use of then-dimensional Green's theorem allows simple generalization of single-parameter methods. Sufficiency is proved under a concavity assumption for the maximized Hamiltonian$$H^\circ (x,\lambda ,t) = \max \{ H(x,u,\lambda ,t):u\varepsilon K\} $$.

关键词： Optimal control distributed-parameter systems control of partial differential equations sufficiency conditions Green's formula

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Identification of distributed-parameter Vibrating systems

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IFAC Proceedings Volumes 1982年第4期15卷 1283-1288页

作者： L. Meirovitch H. Baruh Department of Engineering Science and Mechanics Virginia Polytechnic Institute and State University Blacksburg Virginia USA

This paper describes a method for the identification of the parameters entering into the equations of motion of distributed-para-meter systems. Because the motion of distributed systems is described in terms of partial differential equations, these parameters are in general continuous functions of the spatial variables. For vibrating systems, these parameters ordinarily represent the mass, stiffness and damping distributions. In this paper, these distributions are expanded in terms of finite series of known functions of the spatial variables multiplied by undetermined coefficients. Assuming that the nature of the equations of motion is known and that a limited number of eigenvalues and eigenfunctions is given, use is made of the least-squares method, in conjunction with the eigenfunctions' orthogonality, to compute the undetermined coefficients, thus identifying the system distributed parameters.

关键词： parameter identification distributed-parameter systems partial differential equations vibrating systems mass and stiffness distributions least-squares method

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A Decoupling Approach to the Control of Large Spaceborne Antenna systems

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IFAC Proceedings Volumes 1983年第10期16卷 139-146页

作者： P.K.C. Wang Department of System Science University of California Los Angeles California USA

A simple practical method for designing antenna-feed positioning control systems for large deployable spaceborne antenna systems with flexible booms is proposed. The approach is based on the mechanical decoupling of the antenna-feed from the boom so that the positioning control system can be designed without taking boom dynamics into consideration, thus avoiding a complex infinite dimensional control problem. The basic idea is illustrated by a simple angular positional control system attached to a flexible boom restricted to torsional motion only. The application of this approach to more complex situations is discussed briefly.

关键词： Large space structures distributed-parameter systems decoupling feedback control stability antenna control systems

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PREDICTION OF AIR POLLUTANT CONCENTRATIONS IN TOKUSHIMA PREFECTURE, JAPAN

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AUTOMATICA 1981年第3期17卷 493-508页

作者： YOSHIMURA, T OKAMOTO, Y SOEDA, T Department of Mechanical Engineering Faculty of Engineering Tokushima University Tokushima 770 Minamijosanjima 2-1 Japan

This paper deals with the prediction problem of air pollutant concentrations over the industrial area of Tokushima Prefecture, Japan. The mathematical model used for the prediction of air pollution, which describes the transport and diffusion of pollutants from stack emissions into the atmosphere, is expressed by the three-dimensional partial differential equation known as the advection diffusion model with initial and boundary conditions. Diffusion coefficients characterizing this model are determined effectively from the statistical processing of the available measured data obtained at two monitoring stations. The measured data of sulpher dioxide concentrations are classified by season, weather and wind speed, and then the identification of these coefficients for each class is carried out by using a line search method because of its numerical stability. The estimation theory is extensively applied to this model for obtaining the useful estimates of the spatial and temporal concentration distributions on the basis of actual measured data, in which the analytical solution of this model is given by using the Green's function under some reasonable assumptions and the suitable transformation. The effectiveness of the proposed approach for the prediction of air pollutant is indicated in simulation results.

关键词： Air pollution distributed-parameter systems modelling optimal filtering prediction

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DYNAMIC-PROGRAMMING APPROACH TO THE MAXIMUM PRINCIPLE OF distributed-parameter systems

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1979年第4期27卷 583-601页

作者： FOND, S Transaction Technology Los Angeles

This paper provides a dynamic programming approach to the maximum principle for the optimal control of systems with distributed parameters. The process of the systems under consideration is governed by a partial diffe... 详细信息

关键词： distributed-parameter systems Dynamic programming Frechet derivatives maximum principle optimal control

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distributed-parameter Difference Games with Periodic State Measurements

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IFAC Proceedings Volumes 1980年第6期13卷 315-330页

作者： S.G. Tzafestas Control Systems Laboratory University of Patras Patras Greece Department of Reactors NRC Democritos Aghia Paraskevi Attiki Athens Greece

Recently, differential games have received considerable attention and find applications in both antagonistic and cooperative situations. However the theory has mainly been restricted to lumped-parameter differential or difference games. The purpose of the present paper is to treat difference distributed-parameter (DP) games, i.e. distributed-parameter differential games formulated in discrete time. The Nash strategy is first used, and the open-loop, closed-loop, and open/closed-loop solutions are deri-ved. Then, the more general case of periodic state measurements is considered and the periodic open-loop and periodic open/closed-loop policies are determined. In all cases the solution is found in the form of recursive algorithms based on a series of discrete-time DP equations. Finally, the non-inferior and minimax strategies are employed, and the derivation of the corresponding solutions is outlined. The paper includes an illustrative worst-case-design distributed-parameter nuclear-reactor example.

关键词： Differential games distributed-parameter systems game theory optimal control periodic state measurement schemes

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ACTIVE CONTROL OF FLEXIBLE systems

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1978年第3期25卷 415-436页

作者： BALAS, MJ CHARLES STARK DRAPER LAB INC CAMBRIDGEMA

Since mechanically flexible systems are distributed-parameter systems, they are infinite-dimensional in theory and, in practice, must be modelled by large-dimensional systems. The fundamental problem of actively controlling very flexible systems is to control a large-dimensional system with a much smaller dimensional controller. For example, a large number of elastic modes may be needed to describe the behavior of a flexible satellite; however, active control of all these modes would be out of the question due to onboard computer limitations and modelling error. Consequently, active control must be restricted to a few critical modes. The effect of the residual (uncontrolled) modes on the closed-loop system is often *** this paper, we consider the class of flexible systems that can be described by a generalized wave equation,utt+Au=F, which relates the displacementu(x,t) of a body Θ inn-dimensional space to the applied force distributionF(x,t). The operatorA is a time-invariant symmetric differential operator with a discrete, semibounded spectrum. This class of distributed parameter systems includes vibrating strings, membranes, thin beams, and thin *** control force distribution$$F(x,t) = \sum\limits_{i = 1}^M { \delta (x - x_i )f_i (t)} $$ is provided byM point force actuators located at pointsxi on the body. The displacements (or their velocities) are measured byP point sensorsyi(t)=u(zj,t), orut(zj,t),j=1, 2, ...,P, located at various pointszj along the *** obtain feedback control ofN modes of the flexible system and display the controllability and observability conditions required for successful operation. We examine the control and observation spillover due to the residual modes and show that the combined effect of spillover can lead to instabilities in the closed-loop system. We suggest some remedies for spillover, including a straightforward phase-locked loop prefilter, to remove the instability *** illustrate the concepts of this p

关键词： distributed-parameter systems flexible systems partial differential equations

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EXTREMUM PRINCIPLES FOR OPTIMAL-CONTROL IN NORMED LINEAR-SPACES

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1976年第4期19卷 613-632页

作者： ANDRY, AN WALKER, JA MICHIGAN STATE UNIV DEPT MECH ENGNE LANSINGMI 48823 NORTHWESTERN UNIV DEPT MECH ENGNEVANSTONIL 60201

Extremum principles intended for use in optimal control are derived in the form of necessary conditions and sufficient conditions, formulated in general normed linear spaces. The method of application is illustrated by several examples involving optimal control problems, mathematical programming problems, lumped-parameter systems, and distributed-parameter systems. The basic theorems provide a unified approach which is applicable to a wide variety of problems in open-loop optimal control.

关键词： Extremum principles necessary conditions sufficient conditions optimal controls lumped-parameter systems distributed-parameter systems

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