Reachability Analysis And Deterministic Global Optimization Of Differential Algebraic Systems
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Author | : Achim Ilchmann |
Publisher | : Springer |
Total Pages | : 320 |
Release | : 2015-10-29 |
Genre | : Mathematics |
ISBN | : 331922428X |
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.
Author | : Joseph Kirk Scott |
Publisher | : |
Total Pages | : 460 |
Release | : 2012 |
Genre | : |
ISBN | : |
Systems of differential-algebraic equations (DAEs) are used to model an incredible variety of dynamic phenomena. In the chemical process industry in particular, the numerical simulation of detailed DAE models has become a cornerstone of many core activities including, process development, economic optimization, control system design and safety analysis. In such applications, one is primarily interested in the behavior of the model solution with respect variations in the model inputs or uncertainties in the model itself. This thesis addresses two computational problems of general interest in this regard. In the first, we are interested in computing a guaranteed enclosure of all solutions of a given DAE model subject to a specified set of inputs. This analysis has natural applications in uncertainty quantification and process safety verification, and is used for many important tasks in process control. However, for nonlinear dynamic systems, this task is very difficult. Existing methods apply only to ordinary differential equation (ODE) models, and either provide very conservative enclosures or require excessive computational effort. Here, we present new methods for computing interval bounds on the solutions of ODEs and DAEs. For ODEs, the focus is on efficient methods for using physical information that is often available in applications to greatly reduce the conservatism of existing methods. These methods are then extended for the first time to the class of semi-explicit index-one DAEs. The latter portion of the thesis concerns the global solution of optimization problems constrained by DAEs. Such problems arise in optimal control of batch processes, determination of optimal start-up and shut-down procedures, and parameter estimation for dynamic models. In nearly all conceivable applications, there is significant economic and/or intellectual impetus to locate a globally optimal solution. Yet again, this problem has proven to be extremely difficult for nonlinear dynamic models. A small number of practical algorithms have been proposed, all of which are limited to ODE models and require significant computational effort. Here, we present improved lower-bounding procedures for ODE constrained problems and develop a complete deterministic algorithm for problems constrained by semi-explicit index-one DAEs for the first time.
Author | : Salvador Garcia Munoz |
Publisher | : Elsevier |
Total Pages | : 514 |
Release | : 2019-07-09 |
Genre | : Technology & Engineering |
ISBN | : 0128205717 |
FOCAPD-19/Proceedings of the 9th International Conference on Foundations of Computer-Aided Process Design, July 14 - 18, 2019, compiles the presentations given at the Ninth International Conference on Foundations of Computer-Aided Process Design, FOCAPD-2019. It highlights the meetings held at this event that brings together researchers, educators and practitioners to identify new challenges and opportunities for process and product design. - Combines presentations from the Ninth International Conference on Foundations of Computer-Aided Process Design, FOCAPD-2019
Author | : |
Publisher | : Elsevier |
Total Pages | : 2667 |
Release | : 2015-07-14 |
Genre | : Technology & Engineering |
ISBN | : 0444634452 |
25th European Symposium on Computer-Aided Process Engineering contains the papers presented at the 12th Process Systems Engineering (PSE) and 25th European Society of Computer Aided Process Engineering (ESCAPE) Joint Event held in Copenhagen, Denmark, 31 May - 4 June 2015. The purpose of these series is to bring together the international community of researchers and engineers who are interested in computing-based methods in process engineering. This conference highlights the contributions of the PSE/CAPE community towards the sustainability of modern society. Contributors from academia and industry establish the core products of PSE/CAPE, define the new and changing scope of our results, and future challenges. Plenary and keynote lectures discuss real-world challenges (globalization, energy, environment, and health) and contribute to discussions on the widening scope of PSE/CAPE versus the consolidation of the core topics of PSE/CAPE. - Highlights how the Process Systems Engineering/Computer-Aided Process Engineering community contributes to the sustainability of modern society - Presents findings and discussions from both the 12th Process Systems Engineering (PSE) and 25th European Society of Computer-Aided Process Engineering (ESCAPE) Events - Establishes the core products of Process Systems Engineering/Computer Aided Process Engineering - Defines the future challenges of the Process Systems Engineering/Computer Aided Process Engineering community
Author | : Madhavan Mukund |
Publisher | : Springer |
Total Pages | : 449 |
Release | : 2012-09-28 |
Genre | : Computers |
ISBN | : 3642333869 |
This book constitutes the thoroughly refereed proceedings of the 10th International Symposium on Automated Technology for Verification and Analysis, ATVA 2012, held at Thiruvananthapuram, Kerala, India, in October 2012. The 25 regular papers, 3 invited papers and 4 tool papers presented were carefully selected from numerous submissions. Conference papers are organized in 9 technical sessions, covering the topics of automata theory, logics and proofs, model checking, software verification, synthesis, verification and parallelism, probabilistic verification, constraint solving and applications, and probabilistic systems.
Author | : Thomas Lorenz |
Publisher | : Springer Science & Business Media |
Total Pages | : 526 |
Release | : 2010-06-08 |
Genre | : Language Arts & Disciplines |
ISBN | : 3642124704 |
Ordinary differential equations have been extended to evolution equations in Banach spaces. This book generalizes ordinary differential equations beyond the borders of vector spaces with a focus on the well-posed Cauchy problem in finite time intervals.
Author | : Achim Ilchmann |
Publisher | : Springer |
Total Pages | : 313 |
Release | : 2015-11-06 |
Genre | : Mathematics |
ISBN | : 9783319224275 |
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.
Author | : Lars Grüne |
Publisher | : Springer |
Total Pages | : 241 |
Release | : 2004-10-19 |
Genre | : Mathematics |
ISBN | : 3540367845 |
This book provides an approach to the study of perturbation and discretization effects on the long-time behavior of dynamical and control systems. It analyzes the impact of time and space discretizations on asymptotically stable attracting sets, attractors, asumptotically controllable sets and their respective domains of attractions and reachable sets. Combining robust stability concepts from nonlinear control theory, techniques from optimal control and differential games and methods from nonsmooth analysis, both qualitative and quantitative results are obtained and new algorithms are developed, analyzed and illustrated by examples.
Author | : |
Publisher | : |
Total Pages | : 1518 |
Release | : 2005 |
Genre | : Mathematics |
ISBN | : |
Author | : Lars Grüne |
Publisher | : |
Total Pages | : 248 |
Release | : 2002 |
Genre | : Asymptotes |
ISBN | : 9780540433919 |
This text provides an approach to the study of perturbation and discretization effects on the long-time behaviour of dynamical and control systems. It analyzes the impact of time and space discretizations on asymptotically stable attracting sets, attractors and asumptotically controllable sets.