Control and Optimization with Differential-Algebraic Constraints

Control and Optimization with Differential-Algebraic Constraints PDF

Author: Lorenz T. Biegler

Publisher: SIAM

Published: 2012-01-01

Total Pages: 355

ISBN-13: 9781611972252

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Differential-algebraic equations are the most natural way to mathematically model many complex systems in science and engineering. Once the model is derived, it is important to optimize the design parameters and control it in the most robust and efficient way to maximize performance. This book presents the latest theory and numerical methods for the optimal control of differential-algebraic equations. The following features are presented in a readable fashion so the results are accessible to the widest audience: the most recent theory, written by leading experts from a number of academic and nonacademic areas and departments; several state-of-the-art numerical methods; and real-world applications.

Numerical Methods for Optimal Control Problems with State Constraints

Numerical Methods for Optimal Control Problems with State Constraints PDF

Author: Radoslaw Pytlak

Publisher: Springer

Published: 2006-11-14

Total Pages: 224

ISBN-13: 3540486623

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While optimality conditions for optimal control problems with state constraints have been extensively investigated in the literature the results pertaining to numerical methods are relatively scarce. This book fills the gap by providing a family of new methods. Among others, a novel convergence analysis of optimal control algorithms is introduced. The analysis refers to the topology of relaxed controls only to a limited degree and makes little use of Lagrange multipliers corresponding to state constraints. This approach enables the author to provide global convergence analysis of first order and superlinearly convergent second order methods. Further, the implementation aspects of the methods developed in the book are presented and discussed. The results concerning ordinary differential equations are then extended to control problems described by differential-algebraic equations in a comprehensive way for the first time in the literature.

Practical Methods for Optimal Control Using Nonlinear Programming, Third Edition

Practical Methods for Optimal Control Using Nonlinear Programming, Third Edition PDF

Author: John T. Betts

Publisher: SIAM

Published: 2020-07-09

Total Pages: 748

ISBN-13: 1611976197

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How do you fly an airplane from one point to another as fast as possible? What is the best way to administer a vaccine to fight the harmful effects of disease? What is the most efficient way to produce a chemical substance? This book presents practical methods for solving real optimal control problems such as these. Practical Methods for Optimal Control Using Nonlinear Programming, Third Edition focuses on the direct transcription method for optimal control. It features a summary of relevant material in constrained optimization, including nonlinear programming; discretization techniques appropriate for ordinary differential equations and differential-algebraic equations; and several examples and descriptions of computational algorithm formulations that implement this discretize-then-optimize strategy. The third edition has been thoroughly updated and includes new material on implicit Runge–Kutta discretization techniques, new chapters on partial differential equations and delay equations, and more than 70 test problems and open source FORTRAN code for all of the problems. This book will be valuable for academic and industrial research and development in optimal control theory and applications. It is appropriate as a primary or supplementary text for advanced undergraduate and graduate students.

Mathematical Methods in Optimization of Differential Systems

Mathematical Methods in Optimization of Differential Systems PDF

Author: Viorel Barbu

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 271

ISBN-13: 9401107602

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This work is a revised and enlarged edition of a book with the same title published in Romanian by the Publishing House of the Romanian Academy in 1989. It grew out of lecture notes for a graduate course given by the author at the University if Ia~i and was initially intended for students and readers primarily interested in applications of optimal control of ordinary differential equations. In this vision the book had to contain an elementary description of the Pontryagin maximum principle and a large number of examples and applications from various fields of science. The evolution of control science in the last decades has shown that its meth ods and tools are drawn from a large spectrum of mathematical results which go beyond the classical theory of ordinary differential equations and real analy ses. Mathematical areas such as functional analysis, topology, partial differential equations and infinite dimensional dynamical systems, geometry, played and will continue to play an increasing role in the development of the control sciences. On the other hand, control problems is a rich source of deep mathematical problems. Any presentation of control theory which for the sake of accessibility ignores these facts is incomplete and unable to attain its goals. This is the reason we considered necessary to widen the initial perspective of the book and to include a rigorous mathematical treatment of optimal control theory of processes governed by ordi nary differential equations and some typical problems from theory of distributed parameter systems.

Surveys in Differential-Algebraic Equations III

Surveys in Differential-Algebraic Equations III PDF

Author: Achim Ilchmann

Publisher: Springer

Published: 2015-10-29

Total Pages: 320

ISBN-13: 331922428X

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The present volume comprises survey articles on various fields of Differential-Algebraic Equations (DAEs), which have widespread applications in controlled dynamical systems, especially in mechanical and electrical engineering and a strong relation to (ordinary) differential equations. The individual chapters provide reviews, presentations of the current state of research and new concepts in - Flexibility of DAE formulations - Reachability analysis and deterministic global optimization - Numerical linear algebra methods - Boundary value problems The results are presented in an accessible style, making this book suitable not only for active researchers but also for graduate students (with a good knowledge of the basic principles of DAEs) for self-study.

Applications of Differential-Algebraic Equations: Examples and Benchmarks

Applications of Differential-Algebraic Equations: Examples and Benchmarks PDF

Author: Stephen Campbell

Publisher: Springer

Published: 2019-06-08

Total Pages: 320

ISBN-13: 3030037185

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This volume encompasses prototypical, innovative and emerging examples and benchmarks of Differential-Algebraic Equations (DAEs) and their applications, such as electrical networks, chemical reactors, multibody systems, and multiphysics models, to name but a few. Each article begins with an exposition of modelling, explaining whether the model is prototypical and for which applications it is used. This is followed by a mathematical analysis, and if appropriate, a discussion of the numerical aspects including simulation. Additionally, benchmark examples are included throughout the text. Mathematicians, engineers, and other scientists, working in both academia and industry either on differential-algebraic equations and systems or on problems where the tools and insight provided by differential-algebraic equations could be useful, would find this book resourceful.

Modeling, Control and Optimization of Complex Systems

Modeling, Control and Optimization of Complex Systems PDF

Author: Weibo Gong

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 312

ISBN-13: 1461511399

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Modeling, Control And Optimization Of Complex Systems is a collection of contributions from leading international researchers in the fields of dynamic systems, control theory, and modeling. These papers were presented at the Symposium on Modeling and Optimization of Complex Systems in honor of Larry Yu-Chi Ho in June 2001. They include exciting research topics such as: -modeling of complex systems, -power control in ad hoc wireless networks, -adaptive control using multiple models, -constrained control, -linear quadratic control, -discrete events, -Markov decision processes and reinforcement learning, -optimal control for discrete event and hybrid systems, -optimal representation and visualization of multivariate data and functions in low-dimensional spaces.

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