Representation And Control Of Infinite Dimensional Systems
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Author | : Alain Bensoussan |
Publisher | : Springer Science & Business Media |
Total Pages | : 589 |
Release | : 2007-04-05 |
Genre | : Technology & Engineering |
ISBN | : 0817645810 |
This unified, revised second edition of a two-volume set is a self-contained account of quadratic cost optimal control for a large class of infinite-dimensional systems. The original editions received outstanding reviews, yet this new edition is more concise and self-contained. New material has been added to reflect the growth in the field over the past decade. There is a unique chapter on semigroup theory of linear operators that brings together advanced concepts and techniques which are usually treated independently. The material on delay systems and structural operators has not yet appeared anywhere in book form.
Author | : Alain Bensoussan |
Publisher | : |
Total Pages | : 0 |
Release | : 1992 |
Genre | : Control theory |
ISBN | : 9780817636418 |
Author | : Alain Bensoussan |
Publisher | : |
Total Pages | : 315 |
Release | : 1992 |
Genre | : Control theory |
ISBN | : |
Author | : Alain Bensoussan |
Publisher | : Birkhäuser |
Total Pages | : 0 |
Release | : 2008-11-01 |
Genre | : Technology & Engineering |
ISBN | : 9780817671150 |
This unified, revised second edition of a two-volume set is a self-contained account of quadratic cost optimal control for a large class of infinite-dimensional systems. The original editions received outstanding reviews, yet this new edition is more concise and self-contained. New material has been added to reflect the growth in the field over the past decade. There is a unique chapter on semigroup theory of linear operators that brings together advanced concepts and techniques which are usually treated independently. The material on delay systems and structural operators has not yet appeared anywhere in book form.
Author | : Alain Bensoussan |
Publisher | : Birkhäuser |
Total Pages | : 0 |
Release | : 1993 |
Genre | : Science |
ISBN | : 9781461227502 |
The quadratic cost optimal control problem for systems described by linear ordinary differential equations occupies a central role in the study of control systems both from the theoretical and design points of view. The study of this problem over an infinite time horizon shows the beautiful interplay between optimality and the qualitative properties of systems such as controllability, observability and stability. This theory is far more difficult for infinite-dimensional systems such as systems with time delay and distributed parameter systems. In the first place, the difficulty stems from the essential unboundedness of the system operator. Secondly, when control and observation are exercised through the boundary of the domain, the operator representing the sensor and actuator are also often unbounded. The present book, in two volumes, is in some sense a self-contained account of this theory of quadratic cost optimal control for a large class of infinite-dimensional systems. Volume I deals with the theory of time evolution of controlled infinite-dimensional systems. It contains a reasonably complete account of the necessary semigroup theory and the theory of delay-differential and partial differential equations. Volume II deals with the optimal control of such systems when performance is measured via a quadratic cost. It covers recent work on the boundary control of hyperbolic systems and exact controllability. Some of the material covered here appears for the first time in book form. The book should be useful for mathematicians and theoretical engineers interested in the field of control.
Author | : Alain Bensoussan |
Publisher | : Birkhäuser |
Total Pages | : 348 |
Release | : 1993-01-01 |
Genre | : Science |
ISBN | : 9780817636425 |
The quadratic cost optimal control problem for systems described by linear ordinary differential equations occupies a central role in the study of control systems both from the theoretical and design points of view. The study of this problem over an infinite time horizon shows the beautiful interplay between optimality and the qualitative properties of systems such as controllability, observability and stability. This theory is far more difficult for infinite-dimensional systems such as systems with time delay and distributed parameter systems. In the first place, the difficulty stems from the essential unboundedness of the system operator. Secondly, when control and observation are exercised through the boundary of the domain, the operator representing the sensor and actuator are also often unbounded. The present book, in two volumes, is in some sense a self-contained account of this theory of quadratic cost optimal control for a large class of infinite-dimensional systems. Volume I deals with the theory of time evolution of controlled infinite-dimensional systems. It contains a reasonably complete account of the necessary semigroup theory and the theory of delay-differential and partial differential equations. Volume II deals with the optimal control of such systems when performance is measured via a quadratic cost. It covers recent work on the boundary control of hyperbolic systems and exact controllability. Some of the material covered here appears for the first time in book form. The book should be useful for mathematicians and theoretical engineers interested in the field of control.
Author | : Alain Bensoussan |
Publisher | : |
Total Pages | : 343 |
Release | : 1992 |
Genre | : |
ISBN | : |
Author | : Alain Bensoussan |
Publisher | : |
Total Pages | : 315 |
Release | : 1992 |
Genre | : |
ISBN | : |
Author | : D. Salamon |
Publisher | : |
Total Pages | : 91 |
Release | : 1985 |
Genre | : |
ISBN | : |
The object of these notes is to develop a unifying framework for the functional analytic representation of infinite dimensional linear systems with unbounded input and output operators. On the basis of the general approach new results are derived on the wellposedness of feedback systems and on the linear quadratic control problem. The implications of the theory for large classes of functional and partial differential equations are discussed in detail. Keywords: Representation of infinite dimensional systems, semigroups, boundary control, feedback, linear quadratic control.
Author | : Birgit Jacob |
Publisher | : Springer Science & Business Media |
Total Pages | : 221 |
Release | : 2012-06-13 |
Genre | : Science |
ISBN | : 3034803990 |
This book provides a self-contained introduction to the theory of infinite-dimensional systems theory and its applications to port-Hamiltonian systems. The textbook starts with elementary known results, then progresses smoothly to advanced topics in current research. Many physical systems can be formulated using a Hamiltonian framework, leading to models described by ordinary or partial differential equations. For the purpose of control and for the interconnection of two or more Hamiltonian systems it is essential to take into account this interaction with the environment. This book is the first textbook on infinite-dimensional port-Hamiltonian systems. An abstract functional analytical approach is combined with the physical approach to Hamiltonian systems. This combined approach leads to easily verifiable conditions for well-posedness and stability. The book is accessible to graduate engineers and mathematicians with a minimal background in functional analysis. Moreover, the theory is illustrated by many worked-out examples.