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Identification of distributed parameter systems Using Polynomial Identification Techniques

IFAC Proceedings Volumes 1991年第3期24卷 1145-1150页

作者： P.J. Gawthrop M.T. Nihtilä Department of Mechanical Engineering The University Glasgow G12 8QQ UK Helsinki University of Technology Otakaari 5A SF 02150 Espoo Finland

Certain distributed parameter systems may be approximated by finite dimensional systems which are, however polynomial in unknown parameters. Algorithms are given for estimated unknown parameters of such systems

关键词： parameter estimation recursive es timation distributed-parameter systems least-squares estimation polynomial-in-the-parameter systems

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MAXIMUM PRINCIPLE FOR OPTIMAL-CONTROL OF distributed-parameter systems WITH SINGULAR MASS MATRIX

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1990年第2期66卷 211-226页

作者： SADIGHESFANDIARI, R SLOSS, JM BRUCH, JC UNIV CALIF SANTA BARBARA DEPT MATHSANTA BARBARACA 93106 UNIV CALIF SANTA BARBARA DEPT MECH & ENVIRONM ENGNSANTA BARBARACA 93106

A maximum principle for the open-loop optimal control of a vibrating system relative to a given convex index of performance is investigated. Though maximum principles have been studied by many people (see, e.g., Refs. 1–5), the principle derived in this paper is of particular use for control problems involving mechanical structures. The state variable satisfies general initial conditions as well as a self-adjoint system of partial differential equations together with a homogeneous system of boundary conditions. The mass matrix is diagonal, constant, and singular, and the viscous damping matrix is diagonal. The maximum principle relates the optimal control with the solution of the homogeneous adjoint equation in which terminal conditions are prescribed in terms of the terminal values of the optimal state variable. An application of this theory to a structural vibrating system is given in a companion paper (Ref. 6).

关键词： distributed-parameter systems optimal control maximum principle singular mass matrix

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parameter-IDENTIFICATION FOR PARTIALLY OBSERVED DIFFUSIONS

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1992年第1期75卷 33-50页

作者： DABBOUS, TE AHMED, NU UNIV OTTAWA DEPT ELECT ENGNOTTAWA K1N 6N5ONTARIOCANADA

In this paper, we consider the identification problem of drift and dispersion parameters for a class of partially observed systems governed by Ito equations. Using the pathwise description of the Zakai equation, we formulate the original identification problem as a deterministic control problem in which the unnormalized conditional density (solution of the Zakai equation) is treated as the state, the unknown parameters as controls, and the likelihood ratio as the objective functional. The question of existence of elements in the parameter set that maximize the likelihood ratio is discussed. Further, using variational arguments and the Gateaux differentiability of the unnormalized density on the parameter set, we obtain the necessary conditions for optimal identification.

关键词： NONLINEAR FILTERING LIKELIHOOD RATIO parameter IDENTIFICATION OPTIMAL CONTROL distributed-parameter systems

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2ND-ORDER NECESSARY CONDITIONS IN A DOMAIN OPTIMIZATION PROBLEM

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1990年第2期65卷 223-244页

作者： FUJII, N Department of Control Engineering Faculty of Engineering Science Osaka University Osaka Japan

Second-order necessary conditions of the Kuhn-Tucker type for optimality in a domain optimization problem are studied. The second variation, corresponding to a boundary variation, of the solution to a boundary-value problem is shown to exist and is given as the solution of a boundary-value problem of the same type. The boundary data are shown to be given in terms of the solution and the first variation of the solution. From these results, the second variation of the objective function is calculated to derive second-order necessary conditions of the Kuhn-Tucker type.

关键词： boundary-value problems distributed-parameter systems Domain optimization first and second variations first-order and second-order necessary conditions shape optimal design

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SUBOPTIMALITY AND STABILITY OF LINEAR distributed-parameter systems WITH FINITE-DIMENSIONAL CONTROLLERS

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1985年第1期45卷 1-19页

作者： BALAS, MJ 1.Electrical Computer and Systems Engineering Department Rensselaer Polytechnic Institute Troy New York

In order to implement feedback control for practical distributed-parameter systems (DPS), the resulting controllers must be finite-dimensional. The most natural approach to obtain such controllers is to make a finite-dimensional approximation, i.e., a reduced-order model, of the DPS and design the controller from this. In past work using perturbation theory, we have analyzed the stability of controllers synthesized this way, but used in the actual DPS; however, such techniques do not yield suboptimal performance results easily. In this paper, we present a modification of the above controller which allows us to more properly imbed the controller as part of the DPS. Using these modified controllers, we are able to show a bound on the suboptimality for an optimal quadratic DPS regulator implemented with a finite-dimensional control, as well as stability bounds. The suboptimality result may be regarded as the distributed-parameter version of the 1968 results of Bongiorno and Youla.

关键词： Control theory distributed-parameter systems partial differential equations

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Stabilization of Elastic systems by Means of Computer Vision Feedback

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IFAC Proceedings Volumes 1987年第1期20卷 31-38页

作者： P.K.C. Wang Department of Electrical Engineering University of California Los Angeles CA 90024 USA

In this paper, the use of computer VlSlon in the feedback stabilization of elastic systems arising in large space structures is explored. In particular, a spaceborne antenna with a large flexible reflector surface is considered. First, suppose that the reflector is coated with a light reflecting material, and is illuminated by a light source. From the intensity data of the reflector image obtained by a computer vision system, the displacement and velocity of the surface are estimated using a suitable reflectance model. Next, the estimation of surface motion with the aid of special markings is considered. From the image of the deformed markings, the displacement and velocity of the surface are constructed. Various methods for obtaining stabilizing feedback controls from the estimated displacement and velocity of the surface are discussed. The paper concludes with some experimental observations and a discussion of the application of computer vision feedback in controlling other types of distributed systems

关键词： Feedback stabilization large space structures elastic systems computer vision distributed-parameter systems

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DIGITAL STOCHASTIC-CONTROL OF distributed-parameter systems

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1984年第2期43卷 307-325页

作者： MEIROVITCH, L OZ, H OHIO STATE UNIV DEPT AERONAUT & ASTRONAUT ENGNCOLUMBUSOH 43210

This paper presents a method for discrete-time control and estimation of flexible structures in the presence of actuator and sensor noise. The approach consists of complete decoupling of the modal equations and estimator dynamics based on the independent modal-space control technique and modal spatial filtering of the system output. The solution for the Kalman filter gains reduces to that of independent second-order modal estimators, thus permitting real-time digital control of distributed-parameter systems in a noisy environment. The method can be used to control and estimate any number of modes without computational restraints and is theoretically free of observation spillover. Two examples, the first using nonlinear, quantized control and the second using linear, state feedback control are presented.

关键词： distributed-parameter systems digital control stochastic independent modal-space control independent modal-space Kalman filters

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STOCHASTIC INDEPENDENT MODAL-SPACE CONTROL OF distributed-parameter systems

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1984年第1期44卷 181-185页

作者： TURNER, JD CHUN, HM MIT CAMBRIDGEMA 02139

This reply is concerned with a comment by Turner and Chun on the solution of the matrix Riccati equation used in Ref. 1. Whereas the technique suggested by Turner and Chun may have some numerical advantage over Potter's method in the case of coupled large-order systems, the advantage is minimal when the independent modal-space control method is used.

关键词： Stochastic estimation and control independent modal-space control distributed-parameter systems Potter's method matrix Riccati equation transition matrix

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ON THE PROBLEM OF OBSERVATION SPILLOVER IN SELF-ADJOINT distributed-parameter systems

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1983年第2期39卷 269-291页

作者： MEIROVITCH, L BARUH, H Reynolds Metals Professor Department of Engineering Science and Mechanics Virginia Polytechnic Institute and State University Blacksburg Virginia Assistant Professor Department of Engineering Science and Mechanics Virginia Polytechnic Institute and State University Blacksburg Virginia

The problem of observation spillover in self-adjoint distributed-parameter systems is investigated. Observation spillover occurs when the output of a limited number of sensors, located at various points on the distributed domain, cannot synthesize the modal coordinates exactly. To this end, two techniques of state estimation (namely, observers and modal filters) are described. Both techniques can be used to extract modal coordinates from the system output and to implement feedback controls. It is shown that, if the residual modes are included in the observer dynamics, observation spillover cannot lead to instability in the residual modes. The problem of the unmodeled modes does remain, however. It is also shown that the modal filters have some very attractive features. In particular, modal filters can be designed to estimate the modal coordinates with such accuracy that observation spillover can be virtually eliminated. In addition, when modal filters are used, in conjunction with a sufficiently large number of sensors, the entire infinity of the system modes can be regarded as modeled, which implies that actual distributed control of the system is possible. It is also demonstrated that modal filters are quite easy to design and are not plagued by instability problems.

关键词： Observation spillover distributed-parameter systems state estimation modal filters feedback control controlled and residual modes

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STOCHASTIC INDEPENDENT MODAL-SPACE CONTROL OF distributed-parameter systems

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1983年第1期40卷 121-154页

作者： OZ, H MEIROVITCH, L VIRGINIA POLYTECH INST & STATE UNIV DEPT ENGN SCI & MECHBLACKSBURGVA 24061

A method capable in theory of estimating and controlling all the modes of a distributed-parameter system is presented. A linear distributed estimator using a distributed Kalman function is defined. It is shown that a particular choice of the Kalman function, in conjunction with the independent modal-space control method, leads to an infinite set of independent second-order modal-space Kalman filters cascaded with spatial modal filters. Independent modal-space Kalman filters experience no computational difficulties, regardless of the order of the system, and closed-form solutions for the modal Kalman gain matrices can be obtained with relative ease, making real-time implementation feasible. It is also shown that the independent modal-space Kalman filters are theoretically free of observation spillover.

关键词： Partial differential equations distributed-parameter systems stochastic independent modal-space control independent modal-space Kalman filters spatial modal filters

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