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This volume is the proceedings of the Workshop on Optimal Design and Control that was held in Blacksburg, Virginia, April 8-9, 1994. The workshop was spon­ sored by the Air Force Office of Scientific Research through the Air Force Center for Optimal Design and Control (CODAC) at Virginia Tech. The workshop was a gathering of engineers and mathematicians actively in­ volved in innovative research in control and optimization, with emphasis placed on problems governed by partial differential equations. The interdisciplinary nature of the workshop and the wide range of subdisciplines represented by the partici­ pants enabled an exchange of valuable information and also led to significant dis­ cussions about multidisciplinary optimization issues. One of the goals of the work­ shop was to include laboratory, industrial, and academic researchers so that anal­ yses, algorithms, implementations, and applications could all be well-represented in the talks; this interdisciplinary nature is reflected in these proceedings. An overriding impression that can be gleaned from the papers in this volume is the complexity of problems addressed by not only those authors engaged in appli­ cations, but also by those engaged in algorithmic development and even mathemat­ ical analyses. Thus, in many instances, systematic approaches using fully nonlin­ ear constraint equations are routinely used to solve control and optimization prob­ lems, in some cases replacing ad-hoc or empirically based procedures.

These papers are divided into three parts according to their major emphasis: identification; estimation; and control. Each contribution attempts to cover methodological issues, new problems, approaches and theoretical results, and constructive and numerical techniques.

Periodically Correlated Solutions to a Class of Stochastic Difference Equations.- On Nonlinear SDE'S whose Densities Evolve in a Finite-Dimensional Family.- Composition of Skeletons and Support Theorems.- Invariant Measure for a Wave Equation on a Riemannian Manifold.- Ergodic Distributed Control for Parameter Dependent Stochastic Semilinear Systems.- Dirichlet Forms, Caccioppoli Sets and the Skorohod Equation Masatoshi Fukushima.- Rate of Convergence of Moments of Spall's SPSA Method.- General Setting for Stochastic Processes Associated with Quantum Fields.- On a Class of Semilinear Stochastic Partial Differential Equations.- Parallel Numerical Solution of a Class of Volterra Integro-Differential Equations.- On the Laws of the Oseledets Spaces of Linear Stochastic Differential Equations.- On Stationarity of Additive Bilinear State-space Representation of Time Series.- On Convergence of Approximations of Ito-Volterra Equations.- Non-isotropic Ornstein-Uhlenbeck Process and White Noise Analysis.- Stochastic Processes with Independent Increments on a Lie Group and their Selfsimilar Properties.- Optimal Damping of Forced Oscillations Discrete-time Systems by Output Feedback.- Forecast of Lévy's Brownian Motion as the Observation Domain Undergoes Deformation.- A Maximal Inequality for the Skorohod Integral.- On the Kinematics of Stochastic Mechanics.- Stochastic Equations in Formal Mappings.- On Fisher's Information Matrix of an ARMA Process.- Statistical Analysis of Nonlinear and NonGaussian Time Series.- Bilinear Stochastic Systems with Long Range Dependence in Continuous Time.- On Support Theorems for Stochastic Nonlinear Partial Differential Equations.- Excitation and Performance in Continuous-time Stochastic Adaptive LQ-control.- Invariant Measures for Diffusion Processes in Conuclear Spaces.- Degree Theory on Wiener Space and an Application to a Class of SPDEs.- On the Interacting Measure-Valued Branching Processes.

I. Introduction.- 1. General Overview.- 2. On the Contents of the Book.- II. Modeling of Networks of Elastic Strings.- 1. Modeling of Nonlinear Elastic Strings.- 2. Networks of Nonlinear Elastic Strings.- 3. Linearization.- 4. Well-posedness of the Network Equations.- 5. Controllability of Networks of Elastic Strings.- 5.1. Exact Controllability of Tree Networks.- 5.2. Lack of Controllability for Networks with Closed Circuits.- 6. Stabilizability of String Networks.- 7. String Networks with Masses at the Nodes.- III. Networks of Thermoelastic Beams.- 1. Modeling of a Thin Thermoelastic Curved Beam.- 2. The Equations of Motion.- 2.1. Some Remarks on Warping and Torsion.- 3. Rotating Beams.- 3.1. Dynamic Stiffening.- 4. Straight, Untwisted, Nonshearable Nonlinear 3-d Beams.- 4.1. Approximation-Generalizations.- 5. Straight, Untwisted Shearable Linear 3-d Beams.- 6. Shearable Nonlinear 2-d Beams with Curvature.- 6.1. Approximation-Generalizations.- 7. A List of Beam Models.- Damping.- 8. Networks of Beams.- 8.1. Geometric Joint Conditions.- 8.1.1. Rigid Joints.- 8.1.2. Pinned Joints.- 8.2. Dynamic Joint Conditions.- 8.2.1. Rigid Joints.- 8.2.2. Pinned Joints.- 9. Rotating Two-link Flexible Nonlinear Shearable Beams.- IV. A General Hyperbolic Model for Networks.- 1. The General Model.- 2. Some Special Cases.- 2.1. String Networks.- 2.2. Networks of Planar Timoshenko Beams.- 2.4. Networks of Initially Curved Bresse Beams.- 2.5. Beams and Strings.- 3. Existence and Regularity of Solutions.- 4. Energy Estimates for Hyperbolic Systems.- 5. Exact Controllability of the Network Model.- 6. Stabilizability of the Network Model.- V. Spectral Analysis and Numerical Simulations.- 1. Preliminaries.- 1.1. Notation.- 1.2. Networks of Strings.- 1.3. Networks of Timoshenko Beams.- 1.4. Networks of Euler-Bernoulli Beams.- 2. Eigenvalue Problems for Networks of 1-d Elements.- 2.1. Introduction.- 2.2. General String Networks.- 2.3. Homogeneous String Networks.- 2.3.1. Examples.- 2.4. Networks of Timoshenko Beams.- 2.4.1. The Case Where ? =0.- 2.4.2. The Case Where ? Belongs to an Individual Beam.- 2.4.3. Eigenvalues for the Entire Graph.- 2.5. Homogeneous Timoshenko Networks.- 3. Numerical Simulations of Controlled 1-d Networks.- 3.1. Introductory Remarks.- 3.2. Networks of Strings.- 3.2.1. Absorbing Controls.- 3.2.2. Directing Controls.- 4. Finite Element Approximations of Timoshenko Networks.- 5. Implicit Runge-Kutta Method: Dry Friction at Joints.- VI. Interconnected Membranes.- 1. Modeling of Dynamic Nonlinear Elastic Membranes.- 1.1. Equations of Motion.- 1.2. Edge Conditions.- 1.3. Hamilton's Principle.- 2. Systems of Interconnected Elastic Membranes.- 2.1. Geometric Junction Conditions.- 2.2. Dynamic Conditions.- 2.3. Linearization.- 2.4. Well-Posedness of the Linear Model.- 3. Controllability of Linked Isotropic Membranes.- 3.1. Observability Estimates for the Homogeneous Problem.- 3.2. A Priori Estimates for Serially Connected Membranes.- 3.3. A Priori Estimates for Single Jointed Membrane Systems.- 3.4. The Reachable States.- 3.4.1. Serially Connected Membranes.- 3.4.2. Membrane Transmission Problems.- VII. Systems of Linked Plates.- 1. Modeling of Dynamic Nonlinear Elastic Plates.- 1.1. Equations of Motion.- 1.2. Edge Conditions.- 1.3. Hamilton's Principle.- 1.4. Additional Kinematic and Material Assumptions.- 1.5. Rotations Associated with Plate Deformation.- 2. Linearization.- 2.1. Linearization of Equations of Motion.- 2.2. Linearization of Edge Conditions.- 2.3. Hamilton's Principle for the Reissner Model.- 2.4. Linearization of the Vector Rotation Angle.- 2.5. The Kirchhoff Plate Model.- 3. Systems of Linked Reissner Plates.- 3.1. Geometric Junction Conditions.- 3.2. Linearization of the Geometric Joint Conditions.- 3.3. Dynamic Joint Conditions.- 3.3.1. Dynamic conditions at a connected joint.- 3.3.2. Dynamic conditions at a hinged joint.- 3.3.3. Dynamic conditions at a semi-rigid joint.- 3.3.4. Dynamic conditions at a rigid join...

The Decomposition of Controlled Dynamic Systems.- A Differential Game for the Minimax of a Positional Functional.- Global Methods in Optimal Control Theory.- On the Theory of Trajectory Tubes - a Mathematical Formalism for Uncertain Dynamics, Viability and Control.- A Theory of Generalized Solutions to First-Order PDEs with an Emphasis on Differential Games.- Adaptivity and Robustness in Automatic Control Systems.