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Modelling with Ordinary Differential Equations: A Comprehensive
Approach aims to provide a broad and self-contained introduction to
the mathematical tools necessary to investigate and apply ODE
models. The book starts by establishing the existence of solutions
in various settings and analysing their stability properties. The
next step is to illustrate modelling issues arising in the calculus
of variation and optimal control theory that are of interest in
many applications. This discussion is continued with an
introduction to inverse problems governed by ODE models and to
differential games. The book is completed with an illustration of
stochastic differential equations and the development of neural
networks to solve ODE systems. Many numerical methods are presented
to solve the classes of problems discussed in this book. Features:
Provides insight into rigorous mathematical issues concerning
various topics, while discussing many different models of interest
in different disciplines (biology, chemistry, economics, medicine,
physics, social sciences, etc.) Suitable for undergraduate and
graduate students and as an introduction for researchers in
engineering and the sciences Accompanied by codes which allow the
reader to apply the numerical methods discussed in this book in
those cases where analytical solutions are not available
The sequential quadratic hamiltonian (SQH) method is a novel
numerical optimization procedure for solving optimal control
problems governed by differential models. It is based on the
characterisation of optimal controls in the framework of the
Pontryagin maximum principle (PMP). The SQH method is a powerful
computational methodology that is capable of development in many
directions. The Sequential Quadratic Hamiltonian Method: Solving
Optimal Control Problems discusses its analysis and use in solving
nonsmooth ODE control problems, relaxed ODE control problems,
stochastic control problems, mixed-integer control problems, PDE
control problems, inverse PDE problems, differential Nash game
problems, and problems related to residual neural networks. This
book may serve as a textbook for undergraduate and graduate
students, and as an introduction for researchers in sciences and
engineering who intend to further develop the SQH method or wish to
use it as a numerical tool for solving challenging optimal control
problems and for investigating the Pontryagin maximum principle on
new optimisation problems. Feature Provides insight into
mathematical and computational issues concerning optimal control
problems, while discussing many differential models of interest in
different disciplines. Suitable for undergraduate and graduate
students and as an introduction for researchers in sciences and
engineering. Accompanied by codes which allow the reader to apply
the SQH method to solve many different optimal control and
optimisation problems
Modelling with Ordinary Differential Equations: A Comprehensive
Approach aims to provide a broad and self-contained introduction to
the mathematical tools necessary to investigate and apply ODE
models. The book starts by establishing the existence of solutions
in various settings and analysing their stability properties. The
next step is to illustrate modelling issues arising in the calculus
of variation and optimal control theory that are of interest in
many applications. This discussion is continued with an
introduction to inverse problems governed by ODE models and to
differential games. The book is completed with an illustration of
stochastic differential equations and the development of neural
networks to solve ODE systems. Many numerical methods are presented
to solve the classes of problems discussed in this book. Features:
Provides insight into rigorous mathematical issues concerning
various topics, while discussing many different models of interest
in different disciplines (biology, chemistry, economics, medicine,
physics, social sciences, etc.) Suitable for undergraduate and
graduate students and as an introduction for researchers in
engineering and the sciences Accompanied by codes which allow the
reader to apply the numerical methods discussed in this book in
those cases where analytical solutions are not available
This book provides an introduction to representative
nonrelativistic quantum control problems and their theoretical
analysis and solution via modern computational techniques. The
quantum theory framework is based on the Schroedinger picture, and
the optimization theory, which focuses on functional spaces, is
based on the Lagrange formalism. The computational techniques
represent recent developments that have resulted from combining
modern numerical techniques for quantum evolutionary equations with
sophisticated optimization schemes. Both finite and
infinite-dimensional models are discussed, including the
three-level Lambda system arising in quantum optics, multispin
systems in NMR, a charged particle in a well potential,
Bose-Einstein condensates, multiparticle spin systems, and
multiparticle models in the time-dependent density functional
framework. This self-contained book covers the formulation,
analysis, and numerical solution of quantum control problems and
bridges scientific computing, optimal control and exact
controllability, optimization with differential models, and the
sciences and engineering that require quantum control methods.
This book fills a gap between theory-oriented investigations in
PDE-constrained optimization and the practical demands made by
numerical solutions of PDE optimization problems. The authors
discuss computational techniques representing recent developments
that result from a combination of modern techniques for the
numerical solution of PDEs and for sophisticated optimization
schemes. Computational Optimization of Systems offers readers a
combined treatment of PDE-constrained optimization and
uncertainties and an extensive discussion of multigrid
optimization. It provides a bridge between continuous optimization
and PDE modelling and focuses on the numerical solution of the
corresponding problems. Intended for graduate students in
PDE-constrained optimization, it is also suitable as an
introduction for researchers in scientific computing or
optimization. It will also help researchers in the natural sciences
and engineering to formulate and solve optimization problems.
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Paperback
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R398
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Discovery Miles 3 300
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