Kenneth L. Bowers – författare

The problem of developing a systematic approach to the design of feed­ back strategies capable of shaping the response of complicated dynamical control systems illustrates the integration of a wide variety of mathemat­ ical disciplines typical of the modern theory of systems and control. As a concrete example, one may consider the control of fluid flow across an airfoil, for which recent experiments indicate the possibility of delaying the onset of turbulence by controlling viscosity through thermal actuators located on the airfoil. In general, there are two approaches to the con­ trol of such a complica. ted process, the development of extremely detailed models of the process followed by the derivation of a more "dedicated" feed­ back law or the development of a more simple model class followed by the derivation of control laws which are more robust to unmodelled dynamics and exogeneous disturbances. In either approach, the two twin themes of approximation and computation play a significant role in the derivation and implementation of resulting control laws. And there is no doubt that the cross-fertilization between these twin themes and control theory will increase unabated throughout the next decade, not just as an important component of design and implementation of control laws but also as a source of new problems in computational mathematics. In this volume, we present a collection of papers which were deliv­ ered at the first Bozeman Conference on Computation and Control, held at Montana State University on August 1-11, 1988.

This volume contains a collection of papers delivered by the partici­ pants at the second Conference on Computation and Control held at Mon­ tana State University in Bozeman, Montana from August 1-7, 1990. The conference, as well as this proceedings, attests to the vitality and cohesion between the control theorist and the numerical analyst that was adver­ tised by the first Conference on Computation and Control in 1988. The proceedings of that initial conference was published by Birkhiiuser Boston as the first volume of this same series entitled Computation and Control, Proceedings of the Bozeman Conference, Bozeman, Montana, 1988. Control theory and numerical analysis are both, by their very nature, interdisciplinary subjects as evidenced by their interaction with other fields of mathematics and engineering. While it is clear that new control or es­ timation algorithms and new feedback design methodologies will need to be implemented computationally, it is likewise clear that new problems in computational mathematics arise when implementing a new generation of control algorithms. For these reasons, computational mathematics is mov­ ing to the forefront in recent developments in modern control theory and conversely control theory and its applications continue to be a fertile area for computationalists. This volume contains a representative cross section of the interdisciplinary blend of analytic and numerical techniques that of­ ten occur between advanced control design and practical numerical solution of lumped and distributed parameter systems.

The third Conference on Computation and Control was held at Montana State University in Bozeman, Montana from August 5-11, 1992, and this contains a collection of papers addressing issues including noise abatement via smart material technology, robotic vision and parameter identification.

Here is an elementary development of the Sinc-Galerkin method with the focal point being ordinary and partial differential equations. This is the first book to explain this powerful computational method for treating differential equations. These methods are an alternative to finite difference and finite element schemes, and are especially adaptable to problems with singular solutions. The text is written to facilitate easy implementation of the theory into operating numerical code.The authors' use of differential equations as a backdrop for the presentation of the material allows them to present a number of the applications of the sinc method. Many of these applications are useful in numerical processes of interest quite independent of differential equations. Specifically, numerical interpolation and quadrature, while fundamental to the Galerkin development, are useful in their own right.The intimate connection between collocation and Galerkin for the sinc basis is exposed via sinc-interpolation. The quadrature rules define a class of numerical integration methods that complement better known techniques, which in the case of singular integrands, often require modification. The sinc methodology of the text is illustrated on such applications as initial data recovery, heat diffusion, advective-diffusive transport, and Burgers' equation, to illustrate the numerical implementation of the theory discussed.Engineers may find sinc methods a very competitive approach to the more common boundary element or finite element methods. Further, workers in the signal processing community may find this particular approach a refreshingly different view of the use of sinc functions.Sinc approximation is a relatively new numerical technique. This book provides a much needed elementary level explanation.

The third Conference on Computation and Control was held at Mon­ tana State University in Bozeman, Montana from August 5-11, 1992 and this proceedings represents the evolution that the conference has taken since its 1988 and 1990 predecessors. The first conference and proceedings (Volume 1 in PSCT) nurtured a dialogue between researchers in control theory and the area of numerical computation. This cross-fertilization was continued with the 1990 conference and proceedings (Volume 11 in PSCT) while forecasting the theme for this conference. The present volume contains a collection of papers addressing issues ranging from noise abatement via smart material technology, robotic vi­ sion, and parameter identification to feedback design challenges in fluid control and other areas of topical interest. The area of feedback design in fluid control spawns computational challenges in the form of Burgers'' equation which is addressed both with standard numerical methods as well as new computational procedures. Applications which involve inverse prob­ lems include material parameter estimation and sampling in observability. Whether motivated by the plant or arising as the distributed system in the design of a feedback compensator for problems in nonlinear control, the theme of this conference placed an emphasis on the use of partial dif­ ferential equations in control theory. Through challenges initiated via the control problem or the subsequent computational problem, the joint efforts of experts from the respective disciplines enhance the development of both.

This volume contains a collection of papers delivered by the partici­ pants at the second Conference on Computation and Control held at Mon­ tana State University in Bozeman, Montana from August 1-7, 1990. The conference, as well as this proceedings, attests to the vitality and cohesion between the control theorist and the numerical analyst that was adver­ tised by the first Conference on Computation and Control in 1988. The proceedings of that initial conference was published by Birkhiiuser Boston as the first volume of this same series entitled Computation and Control, Proceedings of the Bozeman Conference, Bozeman, Montana, 1988. Control theory and numerical analysis are both, by their very nature, interdisciplinary subjects as evidenced by their interaction with other fields of mathematics and engineering. While it is clear that new control or es­ timation algorithms and new feedback design methodologies will need to be implemented computationally, it is likewise clear that new problems in computational mathematics arise when implementing a new generation of control algorithms. For these reasons, computational mathematics is mov­ ing to the forefront in recent developments in modern control theory and conversely control theory and its applications continue to be a fertile area for computationalists. This volume contains a representative cross section of the interdisciplinary blend of analytic and numerical techniques that of­ ten occur between advanced control design and practical numerical solution of lumped and distributed parameter systems.

The fourth Conference on Computation and Control was held at Mon­ tana State University in Bozeman, Montana from August 3-9, 1994. These proceedings represent the continued evolution of the cross-disciplinary dia­ logue begun at the 1988 conference (Volume 1 of PSCT) and continued on a biennial basis in 1990 and 1992. Those proceedings are housed in Volume 11 of PSCT and Volume 15 of PSCT, respectively. In recent years considerable effort has been devoted to the problem of developing rigorous numerical methods and computational tools for con­ trol design and analysis. Although computational problems in control are extremely complex, these problems often have special structures that can be exploited to obtain both theoretical and computational results. More­ over, problems that arise from applications are best addressed by interdis­ ciplinary approaches where experts in various disciplines (e. g. numerical analysis, control theory, fluid dynamics) come together and create numer­ ical algorithms specifically for use in control design. This communication not only creates new mathematical tools, it often produces new research problems in the individual disciplines. This conference continues to bring together leading experts in control theory, numerical mathematics and var­ ious application areas to discuss recent developments in interdisciplinary approaches to computational control. The organizers acknowledge the generous support of the Montana State University Foundation, the National Science Foundation''s Division of Mathematical Sciences and the EPSCoR Program (Montana Group for Nonlinear Science).

The problem of developing a systematic approach to the design of feed­ back strategies capable of shaping the response of complicated dynamical control systems illustrates the integration of a wide variety of mathemat­ ical disciplines typical of the modern theory of systems and control. As a concrete example, one may consider the control of fluid flow across an airfoil, for which recent experiments indicate the possibility of delaying the onset of turbulence by controlling viscosity through thermal actuators located on the airfoil. In general, there are two approaches to the con­ trol of such a complica. ted process, the development of extremely detailed models of the process followed by the derivation of a more "dedicated" feed­ back law or the development of a more simple model class followed by the derivation of control laws which are more robust to unmodelled dynamics and exogeneous disturbances. In either approach, the two twin themes of approximation and computation play a significant role in the derivation and implementation of resulting control laws. And there is no doubt that the cross-fertilization between these twin themes and control theory will increase unabated throughout the next decade, not just as an important component of design and implementation of control laws but also as a source of new problems in computational mathematics. In this volume, we present a collection of papers which were deliv­ ered at the first Bozeman Conference on Computation and Control, held at Montana State University on August 1-11, 1988.

The third Conference on Computation and Control was held at Mon­ tana State University in Bozeman, Montana from August 5-11, 1992 and this proceedings represents the evolution that the conference has taken since its 1988 and 1990 predecessors. The first conference and proceedings (Volume 1 in PSCT) nurtured a dialogue between researchers in control theory and the area of numerical computation. This cross-fertilization was continued with the 1990 conference and proceedings (Volume 11 in PSCT) while forecasting the theme for this conference. The present volume contains a collection of papers addressing issues ranging from noise abatement via smart material technology, robotic vi­ sion, and parameter identification to feedback design challenges in fluid control and other areas of topical interest. The area of feedback design in fluid control spawns computational challenges in the form of Burgers' equation which is addressed both with standard numerical methods as well as new computational procedures. Applications which involve inverse prob­ lems include material parameter estimation and sampling in observability. Whether motivated by the plant or arising as the distributed system in the design of a feedback compensator for problems in nonlinear control, the theme of this conference placed an emphasis on the use of partial dif­ ferential equations in control theory. Through challenges initiated via the control problem or the subsequent computational problem, the joint efforts of experts from the respective disciplines enhance the development of both.