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Stability analysis of controlled, partially-connected, distributed-parameter systems through perturbation methods

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2003年第2期116卷 379-392页

作者： Robertson, LM Balas, MJ USAF Res Lab Space Vehicles Directorate Kirtland AFB NM 87117 USA Univ Colorado Dept Aerosp Engn Boulder CO 80309 USA

A stability result for locally-controlled, interconnected, distributed-parameter systems (DPS) is developed. Using a special perturbation operator, exponential stability is shown to be a function of both the value of the perturbation operator and the characteristics of the interconnected DPS. Proof of the bound is shown using the expansion of the matrix operator and the solution vector through a set of gauge functions. Each expansion term is power matched and individually bound using stationary phase methods. Special consideration is given to interconnected systems of a structural dynamic nature.

关键词： distributed-parameter systems perturbation theory induction methods control

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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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Fault detection for linear distributed-parameter systems using finite-dimensional functional observers

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INTERNATIONAL JOURNAL OF CONTROL 2016年第3期89卷 550-563页

作者： Deutscher, Joachim Univ Erlangen Nurnberg Lehrstuhl Regelungstech Cauerstr 7 D-91058 Erlangen Germany

In this article, finite-dimensional residual generators are directly designed for Riesz-spectral systems with bounded input and output operators to detect faults. This is achieved by using finite-dimensional observers, that can estimate linear functionals of the state without spillover. These observers allow for a decoupling of the unknown disturbances from the estimation error dynamics under mild assumptions. Then, a finite-dimensional residual generator is obtained by approximately decoupling the state from the residual, that is generated by the observer states and the outputs. It is shown that the resulting approximation error can be made small by increasing the observer order. Then, fault detection with the finite-dimensional residual generator can be assured by introducing a time-varying threshold. A faulty Euler-Bernoulli beam with structural damping illustrates the proposed finite-dimensional fault detection approach.

关键词： distributed-parameter systems Riesz-spectral systems fault detection functional observer actor faults

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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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Numerical Optimization of Linear, distributed-parameter systems

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1974年第1期14卷 73-98页

作者： Cornick, D. E. Michel, A. N. Martin Marietta Aerosp Corp Denver CO USA Iowa State Univ Dept Elect Engn Ames IA USA

The conjugate gradient method is adapted to the optimization of linear, distributed-parameter systems. The effects of errors introduced by the discretization process are analyzed. Measures for the suboptimality of the numerical solution are established. In order to demonstrate the concepts involved, four specific examples are considered.

关键词： distributed-parameter systems conjugate-gradient methods functional analysis boundary control problems distributed control problems

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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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Hamiltonian formulation of distributed-parameter systems with boundary energy flow

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JOURNAL OF GEOMETRY AND PHYSICS 2002年第1-2期42卷 166-194页

作者： van der Schaft, AJ Maschke, BM Univ Twente Fac Math Sci NL-7500 AE Enschede Netherlands Univ Lyon 1 Lab Automat & Genie Procedes F-69622 Villeurbanne France

A Hamiltonian formulation of classes of distributed-parameter systems is presented, which incorporates the energy flow through the boundary of the spatial domain of the system, and which allows to represent the system as a boundary control Hamiltonian system. The system is Hamiltonian with respect to an infinite-dimensional Dirac structure associated with the exterior derivative and based on Stokes' theorem. The theory is applied to the telegraph equations for an ideal transmission line, Maxwell's equations on a bounded domain with non-zero Poynting vector at its boundary, and a vibrating string with traction forces at its ends. Furthermore, the framework is extended to cover Euler's equations for an ideal fluid on a domain with permeable boundary. Finally, some properties of the Stokes-Dirac structure are investigated, including the analysis of conservation laws. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： distributed-parameter systems Hamiltonian systems boundary variables Dirac structures Stokes' theorem conservation laws

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Optimal control problems with state constraints for semilinear distributed-parameter systems

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1996年第1期88卷 25-59页

作者： Fattorini, HO Professor Department of Mathematics University of California Los Angeles California

We consider optimal control problems for distributed-parameter systems described by semilinear equations, with constraints on the control and on the state, and an exact pointwise target condition. As an application of a general theory of nonlinear programming problems in Banach spaces, a version of the Pontryagin maximum principle is obtained.

关键词： distributed-parameter systems maximum principle optimal control state constraints

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A parametric approach to finite-dimensional control of linear distributed-parameter systems

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INTERNATIONAL JOURNAL OF CONTROL 2010年第8期83卷 1674-1685页

作者： Deutscher, J. Harkort, Ch. Univ Erlangen Nurnberg Lehrstuhl Regelungstech D-91058 Erlangen Germany

This article considers the design of finite-dimensional compensators for distributed-parameter systems using eigenvalue assignment. The proposed compensator consists of an observer estimating additional outputs and a static feedback of the measurable and the estimated outputs. Since the additional outputs can be asymptotically reconstructed, the compensator can be designed using the separation principle, i.e. the closed-loop eigenvalues are given by the observer eigenvalues and the eigenvalues resulting from the static output feedback control. In order to solve the corresponding eigenvalue assignment problem, the parametric approach for the design of static output feedback controllers in finite-dimensions is extended to distributed-parameter systems. By using a parameter optimisation it is possible to assign all closed-loop eigenvalues within specified regions of the complex plane in order to stabilise the system and to assure a desired control performance. A heat conductor is used to demonstrate the proposed design procedure.

关键词： linear systems distributed-parameter systems static output feedback compensator design eigenvalue assignment parameter optimisation

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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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