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An abstract approximation framework and convergence theory for the identification of first and second order nonlinear distributed parameter systems developed previously by the authors and reported on in detail elsewhere are summarized and discussed. The theory is based upon results for systems whose dynamics can be described by monotone operators in Hilbert space and an abstract approximation theorem for the resulting nonlinear evolution system. The application of the theory together with numerical evidence demonstrating the feasibility of the general approach are discussed in the context of the identification of a first order quasi-linear parabolic model for one dimensional heat conduction/mass transport and the identification of a nonlinear dissipation mechanism (i.e., damping) in a second order one dimensional wave equation. Computational and implementational considerations, in particular, with regard to supercomputing, are addressed.

An extension of classical methods of optimal control theory for systems described by ordinary differential equations to distributed-parameter systems described by partial differential equations is presented. An application is given involving the minimum-mass design of a simply-supported shear plate with a fixed fundamental frequency of vibration. An optimal plate thickness distribution in analytical form is found. The case of a minimum-mass design of an elastic sandwich plate whose fundamental frequency of free vibration is fixed. Under the most general conditions, the optimization problem reduces to the solution of two simultaneous partial differential equations involving the optimal thickness distribution and the modal displacement. One equation is the uniform energy distribution expression which was found by Ashley and McIntosh for the optimal design of one-dimensional structures with frequency constraints, and by Prager and Taylor for various design criteria in one and two dimensions. The second equation requires dynamic equilibrium at the preassigned vibration frequency.

An extension of classical methods of optimal control theory for systems described by ordinary differential equations to distributed-parameter systems described by partial differential equations is presented. An application is given involving the minimum-mass design of a simply-supported shear plate with a fixed fundamental frequency of vibration. An optimal plate thickness distribution in analytical form is found. The case of a minimum-mass design of an elastic sandwich plate whose fundamental frequency of free vibration is fixed. Under the most general conditions, the optimization problem reduces to the solution of two simultaneous partial differential equations involving the optimal thickness distribution and the modal displacement. One equation is the uniform energy distribution expression which was found by Ashley and McIntosh for the optimal design of one-dimensional structures with frequency constraints, and by Prager and Taylor for various design criteria in one and two dimensions. The second equation requires dynamic equilibrium at the preassigned vibration frequency.

The investigator surveyed a number of applications and problems motivating his current efforts on numerical techniques for parameter estimation in and optimal control of delay and partial differential equations. He then outlined two different approaches for establishing theoretical convergence results for estimation algorithms. An application of modal techniques to the investigation of transport in brain tissue is briefly explained. A sketch of a convergence theory for spline techniques for function space parameter estimation problems is given.

The 'Conference on Future Directions in Distributed Parameter Systems' brought together experts, whose research represented a broad spectrum of applications quantified by distributed parameter systems, and younger researchers focusing on specific facets of distributed parameter systems. A primary goal of the conference was to establish through plenary lectures the state of the art, open questions and important future research directions in a variety of applications and to pass the perspectives along to researchers in these areas. The conference also facilitated interaction between academic scientists and researchers from government laboratories and industry. The perspectives and recommendations provided in the plenary lectures will be published in a future volume.

Bell System Technical Journal, 45: 7. September 1966 pp 1153-1155. A Stability Criterion for Nonuniformly Sampled and Distributed Parameter Systems. (Kinariwala, B.K.; Gersho, A.)

Bell System Technical Journal, 45: 7. September 1966 pp 1153-1155. A Stability Criterion for Nonuniformly Sampled and Distributed Parameter Systems. (Kinariwala, B.K.; Gersho, A.)

In this project questions related to stabilization of vibrating system by feedback were studied. A vibrating system is uniformly stabilized by a feedback if there is a uniform rate of decay for all vibrational modes of the closed-loop system, which is the system with feedback. Necessary conditions were found for certain kinds of feedback to uniformly stabilize a system which is originally undamped and has the feedback applied at the boundary. Sufficient conditions were found for the feedback to lead to a closed-loop system which is mathematically well-posed. It was also shown that in a large class of systems which are stabilized by feedback, if a small delay is introduced in the computation of the feedback, then the stability of the closed-loop system is destroyed. Keywords: Robust stabilization.

A Chandrasekhar-type factorization method is applied to the linear-quadratic optimal control problem for distributed parameter systems. An aeroelastic control problem is used as a model example to demonstrate that if computationally efficient algorithms, such as those of Chandrasekhar-type, are combined with the special structure often available to a particular problem, then an abstract approximation theory developed for distributed parameter control theory becomes a viable method of solution. A numerical scheme based on averaging approximations is applied to hereditary control problems. Numerical examples are given.

This article is from Bioinformatics , volume 29 . Abstract Summary: Complex computational experiments in Systems Biology, such as fitting model parameters to experimental data, can be challenging to perform. Not only do they frequently require a high level of computational power, but the software needed to run the experiment needs to be usable by scientists with varying levels of computational expertise, and modellers need to be able to obtain up-to-date experimental data resources easily. We have developed a software suite, the Systems Biology Software Infrastructure (SBSI), to facilitate the parameter-fitting process. SBSI is a modular software suite composed of three major components: SBSINumerics, a high-performance library containing parallelized algorithms for performing parameter fitting; SBSIDispatcher, a middleware application to track experiments and submit jobs to back-end servers; and SBSIVisual, an extensible client application used to configure optimization experiments and view results. Furthermore, we have created a plugin infrastructure to enable project-specific modules to be easily installed. Plugin developers can take advantage of the existing user-interface and application framework to customize SBSI for their own uses, facilitated by SBSI’s use of standard data formats.Availability and implementation: All SBSI binaries and source-code are freely available from http://sourceforge.net/projects/sbsi under an Apache 2 open-source license. The server-side SBSINumerics runs on any Unix-based operating system; both SBSIVisual and SBSIDispatcher are written in Java and are platform independent, allowing use on Windows, Linux and Mac OS X. The SBSI project website at http://www.sbsi.ed.ac.uk provides documentation and tutorials.Contact: [email protected] information: Supplementary data are available at Bioinformatics online.

This article is from Bioinformatics , volume 29 . Abstract Summary: Complex computational experiments in Systems Biology, such as fitting model parameters to experimental data, can be challenging to perform. Not only do they frequently require a high level of computational power, but the software needed to run the experiment needs to be usable by scientists with varying levels of computational expertise, and modellers need to be able to obtain up-to-date experimental data resources easily. We have developed a software suite, the Systems Biology Software Infrastructure (SBSI), to facilitate the parameter-fitting process. SBSI is a modular software suite composed of three major components: SBSINumerics, a high-performance library containing parallelized algorithms for performing parameter fitting; SBSIDispatcher, a middleware application to track experiments and submit jobs to back-end servers; and SBSIVisual, an extensible client application used to configure optimization experiments and view results. Furthermore, we have created a plugin infrastructure to enable project-specific modules to be easily installed. Plugin developers can take advantage of the existing user-interface and application framework to customize SBSI for their own uses, facilitated by SBSI’s use of standard data formats.Availability and implementation: All SBSI binaries and source-code are freely available from http://sourceforge.net/projects/sbsi under an Apache 2 open-source license. The server-side SBSINumerics runs on any Unix-based operating system; both SBSIVisual and SBSIDispatcher are written in Java and are platform independent, allowing use on Windows, Linux and Mac OS X. The SBSI project website at http://www.sbsi.ed.ac.uk provides documentation and tutorials.Contact: [email protected] information: Supplementary data are available at Bioinformatics online.

The problem we consider in this work is to minimize the L^q-norm (q > 2) of the semidiscrete controls. As shown in [LT06], under the main approximation assumptions that the discretized semigroup is uniformly analytic and that the degree of unboundedness of control operator is lower than 1/2, the uniform controllability property of semidiscrete approximations for the parabolic systems is achieved in L^2. In the present paper, we show that the uniform controllability property still continue to be asserted in L^q. (q > 2) even with the con- dition that the degree of unboundedness of control operator is greater than 1/2. Moreover, the minimization procedure to compute the ap- proximation controls is provided. An example of application is imple- mented for the one dimensional heat equation with Dirichlet boundary control.

The main purpose of this research is to develop a rigorous mathematical framework for the design of control laws for feedback stabilization and for controllability of the transient behavior of flexible structures based on distributed parameter models of such structures. This work has entailed deriving accurate distributed parameter models for elastic structures and understanding the implications of the various models for the controllability and stabilizability of structures. Substantial progress has been made for models of multiple-link constructions that are composed of elastic beams, plates., shells or combinations of such elastic elements. Such structures are representative of trusses, frames, robot arms, solar panels, antennae, deformable mirrors, etc., currently in use.

Methods for estimating system parameters are discussed for a class of partial differential equations. We develop schemes based on modal subspace approximations in some detail and include numerical examples. (Author)

Information is given in viewgraph form on the modeling of nonlinear damping in distributed parameter systems.

A digital distributed parameter model for computing the dynamic response of propellant feed systems is formulated. The analytical approach used is an application of the wave-plan method of analyzing unsteady flow. Nonlinear effects are included. The model takes into account locally high compliances at the pump inlet and at the injector dome region. Examples of the calculated transient and steady-state periodic responses of a simple hypothetical propellant feed system to several types of disturbances are presented. Included are flow disturbances originating from longitudinal structural motion, gimbaling, throttling, and combustion-chamber coupling. The analytical method can be employed for analyzing developmental hardware and offers a flexible tool for the calculation of unsteady flow in these systems.

Theoretical results that enable rigorous statements of convergence and exponential stability of Galerkin approximations of LQR controls for infinite dimensional, or distributed parameter, systems have proliferated over the past ten years. In addition, extensive progress has been made over the same time period in the derivation of robust control design strategies for finite dimensional systems. However, the study of the convergence of robust finite dimensional controllers to robust controllers for infinite dimensional systems remains an active area of research. We consider a class of soft-constrained differential games evolving in a Hilbert space. Under certain conditions, a saddle point control can be given in feedback form in terms of a solution to a Riccati equation. By considering a related LQR problem, we can show a convergence result for finite dimensional approximations of this differential game. This yields a computational algorithm for the feedback gain that can be derived from similar strategies employed in infinite dimensional LQR control design problems. The approach described in this paper also inherits the additional properties of stability robustness common to game theoretic methods in finite dimensional analysis. These theoretical convergence and stability results are verified in several numerical experiments.

The problem of estimating spatially varying coefficients of partial differential equations is considered from observation of the solution and of the right hand side of the equation. It is assumed that the observations are distributed in the domain and that enough observations are given. A method of discretization and an efficient multigrid method for solving the resulting discrete systems are described. Numerical results are presented for estimation of coefficients in an elliptic and a parabolic partial differential equation.

This paper considers the distributed robust control problems of uncertain linear multi-agent systems with undirected communication topologies. It is assumed that the agents have identical nominal dynamics while subject to different norm-bounded parameter uncertainties, leading to weakly heterogeneous multi-agent systems. Distributed controllers are designed for both continuous- and discrete-time multi-agent systems, based on the relative states of neighboring agents and a subset of absolute states of the agents. It is shown for both the continuous- and discrete-time cases that the distributed robust control problems under such controllers in the sense of quadratic stability are equivalent to the $H_\infty$ control problems of a set of decoupled linear systems having the same dimensions as a single agent. A two-step algorithm is presented to construct the distributed controller for the continuous-time case, which does not involve any conservatism and meanwhile decouples the feedback gain design from the communication topology. Furthermore, a sufficient existence condition in terms of linear matrix inequalities is derived for the distributed discrete-time controller. Finally, the distributed robust $H_\infty$ control problems of uncertain linear multi-agent systems subject to external disturbances are discussed.

In this paper, we model and solve the problem of designing in an optimal way actuators for parabolic partial differential equations settled on a bounded open connected subset $\Omega$ of IR n. We optimize not only the location but also the shape of actuators, by finding what is the optimal distribution of actuators in $\Omega$, over all possible such distributions of a given measure. Using the moment method, we formulate a spectral optimal design problem, which consists of maximizing a criterion corresponding to an average over random initial data of the largest L 2-energy of controllers. Since we choose the moment method to control the PDE, our study mainly covers one-dimensional parabolic operators, but we also provide several examples in higher dimensions. We consider two types of controllers: either internal controls, modeled by characteristic functions, or lumped controls, that are tensorized functions in time and space. Under appropriate spectral assumptions, we prove existence and uniqueness of an optimal actuator distribution, and we provide a simple computation procedure. Numerical simulations illustrate our results.

Here an original idea is suggested to prove the existence of optimal control for some types of non- linear problems. The obtained results can be considered as individual existence theorems (in some sense).

In the analysis of vibrations of continuous elastic systems, one often encounters complicated transcendental equations with roots directly related to the system's natural frequencies. Typically, these equations contain system parameters whose values must be specified before a numerical solution can be obtained. The present paper presents a method whereby the fundamental frequency can be obtained in analytical form to any desired degree of accuracy. The method is based upon truncation of rapidly converging series involving inverse powers of the system natural frequencies. A straightforward method to developing these series and summing them in closed form is presented. It is demonstrated how Computer Algebra can be exploited to perform the intricate analytical procedures which otherwise would render the technique difficult to apply in practice. We illustrate the method by developing two analytical approximations to the fundamental frequency of a vibrating cantilever carrying a rigid tip body. The results are compared to the numerical solution of the exact (transcendental) frequency equation over a range of system parameters.

Cyber-physical systems (CPSs) are man-made complex systems coupled with natural processes that, as a whole, should be described by distributed parameter systems (DPSs) in general forms. This paper presents three such general models for generalized DPSs that can be used to characterize complex CPSs. These three different types of fractional operators based DPS models are: fractional Laplacian operator, fractional power of operator or fractional derivative. This research investigation is motivated by many fractional order models describing natural, physical, and anomalous phenomena, such as sub-diffusion process or super-diffusion process. The relationships among these three different operators are explored and explained. Several potential future research opportunities are then articulated followed by some conclusions and remarks.

Cyber-physical systems (CPSs) are man-made complex systems coupled with natural processes that, as a whole, should be described by distributed parameter systems (DPSs) in general forms. This paper presents three such general models for generalized DPSs that can be used to characterize complex CPSs. These three different types of fractional operators based DPS models are: fractional Laplacian operator, fractional power of operator or fractional derivative. This research investigation is motivated by many fractional order models describing natural, physical, and anomalous phenomena, such as sub-diffusion process or super-diffusion process. The relationships among these three different operators are explored and explained. Several potential future research opportunities are then articulated followed by some conclusions and remarks.

Cyber-physical systems (CPSs) are man-made complex systems coupled with natural processes that, as a whole, should be described by distributed parameter systems (DPSs) in general forms. This paper presents three such general models for generalized DPSs that can be used to characterize complex CPSs. These three different types of fractional operators based DPS models are: fractional Laplacian operator, fractional power of operator or fractional derivative. This research investigation is motivated by many fractional order models describing natural, physical, and anomalous phenomena, such as sub-diffusion process or super-diffusion process. The relationships among these three different operators are explored and explained. Several potential future research opportunities are then articulated followed by some conclusions and remarks.

Cyber-physical systems (CPSs) are man-made complex systems coupled with natural processes that, as a whole, should be described by distributed parameter systems (DPSs) in general forms. This paper presents three such general models for generalized DPSs that can be used to characterize complex CPSs. These three different types of fractional operators based DPS models are: fractional Laplacian operator, fractional power of operator or fractional derivative. This research investigation is motivated by many fractional order models describing natural, physical, and anomalous phenomena, such as sub-diffusion process or super-diffusion process. The relationships among these three different operators are explored and explained. Several potential future research opportunities are then articulated followed by some conclusions and remarks.

Efforts to develop computational methods for the identification and optimal control of linear and nonlinear systems governed by distributed parameter systems are reported on. Specifically, approximation methods for determining Optimal LOG compensators (feedback control and estimator gains) and functional parameters in linear and nonlinear partial differential equations and hereditary systems were developed, analyzed and tested. The study included theoretical, experimental and numerical components. Covergence theories for spline-based and modal finite element schemes were established and extensive numerical studies on both conventional (serial) and vector supercomputers were carried out. A parameter estimation scheme was tested using experimental data taken from the RPL structure, a laboratory experiment designed to test control algorithms for the large angle slewing of spacecraft with flexible appendages, and other projects involving the identification of flexible structures based upon experimental data were initiated.

This theses considers the problem of robustly stabilizing infinite-dimensional systems using finite-dimensional controllers. The controllers are assumed to be linear quadratic Gaussian (LQG) based controllers. This research uses a direct approach to demonstrate the existence of finite-dimensional LQG-based controllers that stabilize the nominal system. Once existence is proven, the research focuses on ways to analyze the robustness of the controller. Several types of perturbations are considered, including bounded, relatively bounded, additive, and multiplicative. Several approaches to analyzing robustness are developed. Direct analysis using results from functional analysis is accomplished, followed by an approach called the optimal projection equation approach, and then H-infinity techniques are used to develop a sufficient condition for robustness in the presence of multiplicative perturbations of the plant transfer function. A new interpretation of the linear quadratic Gaussian/loop transfer recovery technique (LQG/LTR) is made for the case of reduced order controllers.

The solution of the sparse algebraic system for a point controlled elliptic distributed parameter system by a multiple shooting and sweep algorithm is discussed. The multiple shooting and sweep algorithm enhances the convergence rate of the ordinary shooting method while achieving a significant reduction in the dimension of the linear equations to be solved. The optimization algorithm for a special problem involving the minimum cost selection of source intensities with the state satisfying a specified constraint set is presented. An application of the techniques involving the analysis and management design for water quality control in Corpus Christi Bay, an estuary on the Texas Gulf Coast in the United States, is discussed. The resulting algorithm is more than twice as fast as a corresponding successive overrelaxation method. (Author)

Results on symmetrizable nonselfadjoint distributed parameter systems are reported on. Operator factorizations are used to characterize the dynamics of a subclass of non-conservative and nonselfadjoint linear distributed parameter systems modeled by partial differential equations subject to various boundary conditions. The results are used to characterize the dynamics of such systems. In addition, the control problem of the validity of using a finite dimensional model in designing a control law for such systems is discussed in terms of stabilization and convergence. In addition, results on damping ratios and on thermal runaway in strain heating has been determined. Also bounds on decay rates for various finite dimensional versions of structures have been derived.

This report describes progress in the development and application of H-infinity-optimal control theory to distributed parameter systems. This research is intended to develop both theory and algorithms capable of providing realistic control systems for physical plants which are appropriately modeled as infinite dimensional linear systems, such as large space structures. In pursuing this program, we have focused on issues motivated by specific models of infinite dimensional systems. Our main results are as follows: We have extended outer factor absorption results to cover certain irrational outer factors. This is in order to justify transformations used in a step for further explicit solution. We have generalized previous results on the single-input/single-output (SISO) mixed sensitivity problem to the case of irrational outer factor and unstable plant. We have solved a multi-input/output mixed sensitivity problem which cannot be treated by previous results. Finally, we developed a technique for numerically computing the optimal value of weighted mixed sensitivity for SISO systems, for the case where explicit symbolic inner/outer factorizations are not possible.

This report describes progress in the development and application of H-infinity-optimal control theory to distributed parameter systems. This research is intended to develop both theory and algorithms capable of providing realistic control systems for physical plants which are appropriately modeled as infinite dimensional linear systems, such as large space structures. In pursuing this program, we have focused on issues motivated by specific models of infinite dimensional systems. Our main results are as follows: We have extended outer factor absorption results to cover certain irrational outer factors. This is in order to justify transformations used in a step for further explicit solution. We have generalized previous results on the single-input/single-output (SISO) mixed sensitivity problem to the case of irrational outer factor and unstable plant. We have solved a multi-input/output mixed sensitivity problem which cannot be treated by previous results. Finally, we developed a technique for numerically computing the optimal value of weighted mixed sensitivity for SISO systems, for the case where explicit symbolic inner/outer factorizations are not possible.

Parabolic partial differential equations for optimal pointwise feedback control of distributed parameter systems

Controllability of distributed-parameter control systems is mathematically studied. A general theory for control systems includes those that cannot be described by ordinary differential equations.

We study one-dimensional integral inequalities, with quadratic integrands, on bounded domains. Conditions for these inequalities to hold are formulated in terms of function matrix inequalities which must hold in the domain of integration. For the case of polynomial function matrices, sufficient conditions for positivity of the matrix inequality and, therefore, for the integral inequalities are cast as semi-definite programs. The inequalities are used to study stability of linear partial differential equations.

The numerical optimization of distributed parameter systems is considered. In particular the adaptation of the Davidon method, the conjugate gradient method, and the best step steepest descent method to distributed parameters is presented. The class of problems with quadratic cost functionals and linear dynamics is investigated. Penalty functions are used to render constrained problems amenable to these gradient techniques. Also considered is an analysis of the effects of discretization of continuous distributed parameter optimal control problems. Estimates of discretization error bounds are established and a measure of the suboptimality of the numerical solution is presented.

The Chandrasekhar equations arising in optimal control problems for linear distributed parameter systems are considered. The equations are derived via approximation theory. This approach is used to obtain existence, uniqueness, and strong differentiability of the solutions and provides the basis for a convergent computation scheme for approximating feedback gain operators. A numerical example is presented to illustrate these ideas.

A theoretical framework is presented that can be used to treat approximation techniques for very general classes of parameter estimation problems involving distributed systems that are either first or second order in time. Using the approach developed, one can obtain both convergence and stability (continuous dependence of parameter estimates with respect to the observations) under very weak regularity and compactness assumptions on the set of admissible parameters. This unified theory can be used for many problems found in the recent literature and in many cases offers significant improvements to existing results.

This research has developed a number of new results for the modeling and control of spatially continuous dynamic processes. The work includes developing numerical methods for implementing controller designs for those linear and nonlinear partial differential equations that describe the dynamics of fluid/structure systems and thermo-mechanical alloys.

The reduced order model problem in distributed parameter systems adaptive identification and control is investigated. A comprehensive examination of real-time centralized adaptive control options for flexible spacecraft is provided.

The reduced order model problem in distributed parameter systems adaptive identification and control is investigated. A comprehensive examination of real-time centralized adaptive control options for flexible spacecraft is provided.

The research concerning the reduced order model problem in distributed parameter systems is reported. The adaptive control strategy was chosen for investigation in the annular momentum control device. It is noted, that if there is no observation spill over, and no model errors, an indirect adaptive control strategy can be globally stable. Recent publications concerning adaptive control are included.

Frequency response and design of distributed parameter networks using asymptotic approximation

The efficient numerical treatment of optimal control problems governed by elliptic partial differential equations (PDEs) and systems of elliptic PDEs, where the control is finite dimensional is discussed. Distributed control as well as boundary control cases are discussed. The main characteristic of the new methods is that they are designed to solve the full optimization problem directly, rather than accelerating a descent method by an efficient multigrid solver for the equations involved. The methods use the adjoint state in order to achieve efficient smoother and a robust coarsening strategy. The main idea is the treatment of the control variables on appropriate scales, i.e., control variables that correspond to smooth functions are solved for on coarse grids depending on the smoothness of these functions. Solution of the control problems is achieved with the cost of solving the constraint equations about two to three times (by a multigrid solver). Numerical examples demonstrate the effectiveness of the method proposed in distributed control case, pointwise control and boundary control problems.

This paper studies distributed-parameter systems on Riemannian manifolds with respect to Stokes-Dirac structures in a language of contact geometry with fiber bundles. For the class where energy functionals are quadratic, it is shown that distributed-parameter port-Hamiltonian systems with respect to Stokes-Dirac structures on one, two, and three dimensional Riemannian manifolds are written in terms of contact Hamiltonian vector fields on bundles. Their fiber spaces are contact manifolds and base spaces are Riemannian manifolds. In addition, for a class of distributed-parameter port-Hamiltonian systems, information geometry induced from contact manifolds and convex energy functionals is introduced and briefly discussed.

This paper studies distributed-parameter systems on Riemannian manifolds with respect to Stokes-Dirac structures in a language of contact geometry with fiber bundles. For the class where energy functionals are quadratic, it is shown that distributed-parameter port-Hamiltonian systems with respect to Stokes-Dirac structures on one, two, and three dimensional Riemannian manifolds are written in terms of contact Hamiltonian vector fields on bundles. Their fiber spaces are contact manifolds and base spaces are Riemannian manifolds. In addition, for a class of distributed-parameter port-Hamiltonian systems, information geometry induced from contact manifolds and convex energy functionals is introduced and briefly discussed.

This research was concerned with analytical results related to control of distributed parameter systems. Existence of optimal controls was established for a variety of systems governed by partial differential equations, most of which involved boundary control. Much of the work also dealt nonlinearity. The work on switching systems promises to provide a theoretical baais for dealing under this grant, including A class of stabilizing feedback laws for marginally stable systems answers the question of how costly it is (in terms of control energy) to control quickly. Keywords: Reports; Abstracts.

This instrumentation award funded the purchase of a laser vibrometer system, mass computer data storage and data acquisition equipment. This equipment used in conjunction with existing vibration testing and control facilities provides a sophisticated low frequency velocity measurement system for use in identifying the coefficients in partial differential equation models of distributed mass structures. In addition, the vibrometer system provides straightforward and direct velocity feedback for such systems. These flexible structures characteristically have very low natural frequencies which cannot be detected by accelerometers. This system has and is being used to perform tests on models and sub-assemblies of large space structures for the purpose of evaluating existing identification and control strategies as well as to stimulate new research in the area of control, observers (estimators) and identification. Several intense experiments using the laser vibrometer were performed to measure the response of a quasi isotropic cantilevered beam with a removable tip mass excited by an impulse at various locations. This data was collected, stored, and sent to AFOSR researchers at Brown University transmitted using BITNET. The data was analyzed using a spline based estimation procedure, starting with a partial differential equation model of the structure. A clear advantage over modal methods based on a finite dimensional model of the same system was observed. (JHD)

This research seeks to unify certain problems of distributed parameter control: model reduction, control, sensor/actuator selections/failure, and decentralized control. These topics are all related and are to be unified through the quadric performance metric with use of cost decomposition methods. The final research topic on model error estimation is required to male vernier adjustments after best models and controllers are developed, to absorb remaining modeling errors. During the period covered by the grant, 16 conference and journal research papers were written. Titles include: Computer Aided Design of Suboptimal LQG Controller, Cost Equivalent Realizations of Stochastic Processes, Component Cost Analysis of Large Scale Systems, Comments on Realizations and Reduction of Markovian Models for Nonstationary Data, and On the Selection of Controller Order for the Control of Linear Dynamic Systems.