Download or read book The SQP method for optimal control problems with mixed constraints written by Nataliya Metla and published by Sudwestdeutscher Verlag Fur. This book was released on 2009-01 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many scientific and technical processes are described by partial differential equations. The optimization of such processes leads to optimal control problems for partial differential equations. Focus of interest in present work is a family of optimal control problems governed by semilinear elliptic partial differential equations (PDEs) and pointwise nonlinear inequality constraints. In order to find an optimal solution, one puts special attention to numerical methods. In the scope of present dissertation, we establish necessary and sufficient optimality conditions and analyze the convergence of sequential quadratic programming (SQP) methods applied to mixed constrained optimal control problems, i.e., for the optimal control problem with coupling between control and state in constraints. The convergence theory for the SQP method bases on its relation to the Newton method applied to a so-called generalized equation which represents first-order necessary optimality conditions. At the end of this thesis the developed theory is verified by numerical tests for discrete optimal control problems.
Download or read book Numerical Solution of Optimal Control Problems with State Constraints by Sequential Quadratic Programming in Function Space written by Kees C. P. Machielsen and published by . This book was released on 1988 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Adaptive SQP Method with Reduced Order Models for Optimal Control Problems with Constraints on the State Applied to the Navier Stokes Equations written by Stefanie Marita Bott and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fast Solution of Discretized Optimization Problems written by Karl-Heinz Hoffmann and published by Birkhäuser. This book was released on 2012-12-06 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of articles summarizing the state of knowledge in a large portion of modern homotopy theory. This welcome reference for many new results and recent methods is addressed to all mathematicians interested in homotopy theory and in geometric aspects of group theory.
Download or read book Numerical Methods for Optimal Control Problems with State Constraints written by Radoslaw Pytlak and published by Springer. This book was released on 2006-11-14 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Optimal Control of ODEs and DAEs written by Matthias Gerdts and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-11-06 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Adaptive Discretization and Sequential Linear Quadratic Strategies in Optimal Control written by Luis Alberto Rodriguez and published by . This book was released on 2010 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: In disciplines such as robotics and aerospace engineering, there is an increasing demand to find control policies that maximize system performance specified in terms of decreasing effort, reducing fuel consumption, or generating graceful motions to achieve complex tasks. Such objectives can be expressed in terms of a scalar cost function that must be minimized subject to various physical constraints. Due to the importance of solving these optimal control problems, numerous algorithms have been proposed. A common approach employed in many of these algorithms is to discretize the continuous-time problem and obtain a finite-dimensional nonlinear problem that can be solved using a general-purpose nonlinear optimization solver. However, casting the problem in this manner destroys the inherent structure of the optimal control problem and results in large-scale problems that are computationally expensive to solve. Another problem is that the choice of an appropriate discretization to accurately represent the solution is left entirely to the expertise of the user. As a consequence, inefficient discretization schemes are often chosen that either do not provide sufficient control resolution to capture important characteristics such as discontinuities or are too dense, requiring intense computational effort. To address these issues, we propose a Runge-Kutta based algorithm that iteratively solves a sequence of discrete-time optimal control problems (DT-OCP) that consistently approximate the continuous-time optimal control problem. To solve these DT-OCPs efficiently we developed a custom SQP method which we refer to as the Constrained Sequential Linear Quadratic (CSLQ) algorithm. The SQP algorithm handles general inequality path constraints including mixed state-control and state-only constraints, preserves the structure of the optimal control problem and exhibits favorable computational complexities with respect to the problem variables. The efficiency of the CSLQ is derived from the implementation of a Riccati based active-set method for solving general inequality constrained linear quadratic optimal control problems. The associated difficulties in selecting an adequate time discretization grid are alleviated by the implementation of a sensitivity-based adaptive algorithm that efficiently refines the discretization by examining where the largest violations in the optimality conditions occur.
Download or read book Practical Methods for Optimal Control and Estimation Using Nonlinear Programming written by John T. Betts and published by SIAM. This book was released on 2010-01-01 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book describes how sparse optimization methods can be combined with discretization techniques for differential-algebraic equations and used to solve optimal control and estimation problems. The interaction between optimization and integration is emphasized throughout the book.
Download or read book Advances in Mathematical Modeling Optimization and Optimal Control written by Jean-Baptiste Hiriart-Urruty and published by Springer. This book was released on 2016-05-19 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains extended, in-depth presentations of the plenary talks from the 16th French-German-Polish Conference on Optimization, held in Kraków, Poland in 2013. Each chapter in this book exhibits a comprehensive look at new theoretical and/or application-oriented results in mathematical modeling, optimization, and optimal control. Students and researchers involved in image processing, partial differential inclusions, shape optimization, or optimal control theory and its applications to medical and rehabilitation technology, will find this book valuable. The first chapter by Martin Burger provides an overview of recent developments related to Bregman distances, which is an important tool in inverse problems and image processing. The chapter by Piotr Kalita studies the operator version of a first order in time partial differential inclusion and its time discretization. In the chapter by Günter Leugering, Jan Sokołowski and Antoni Żochowski, nonsmooth shape optimization problems for variational inequalities are considered. The next chapter, by Katja Mombaur is devoted to applications of optimal control and inverse optimal control in the field of medical and rehabilitation technology, in particular in human movement analysis, therapy and improvement by means of medical devices. The final chapter, by Nikolai Osmolovskii and Helmut Maurer provides a survey on no-gap second order optimality conditions in the calculus of variations and optimal control, and a discussion of their further development.
Download or read book Constrained Optimization and Optimal Control for Partial Differential Equations written by Günter Leugering and published by Springer Science & Business Media. This book was released on 2012-01-03 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: This special volume focuses on optimization and control of processes governed by partial differential equations. The contributors are mostly participants of the DFG-priority program 1253: Optimization with PDE-constraints which is active since 2006. The book is organized in sections which cover almost the entire spectrum of modern research in this emerging field. Indeed, even though the field of optimal control and optimization for PDE-constrained problems has undergone a dramatic increase of interest during the last four decades, a full theory for nonlinear problems is still lacking. The contributions of this volume, some of which have the character of survey articles, therefore, aim at creating and developing further new ideas for optimization, control and corresponding numerical simulations of systems of possibly coupled nonlinear partial differential equations. The research conducted within this unique network of groups in more than fifteen German universities focuses on novel methods of optimization, control and identification for problems in infinite-dimensional spaces, shape and topology problems, model reduction and adaptivity, discretization concepts and important applications. Besides the theoretical interest, the most prominent question is about the effectiveness of model-based numerical optimization methods for PDEs versus a black-box approach that uses existing codes, often heuristic-based, for optimization.
Download or read book Fast Numerical Methods for Mixed Integer Nonlinear Model Predictive Control written by Christian Kirches and published by Springer Science & Business Media. This book was released on 2011-11-23 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Christian Kirches develops a fast numerical algorithm of wide applicability that efficiently solves mixed-integer nonlinear optimal control problems. He uses convexification and relaxation techniques to obtain computationally tractable reformulations for which feasibility and optimality certificates can be given even after discretization and rounding.
Download or read book Optimization with PDE Constraints written by Michael Hinze and published by Springer Science & Business Media. This book was released on 2008-10-16 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solving optimization problems subject to constraints given in terms of partial d- ferential equations (PDEs) with additional constraints on the controls and/or states is one of the most challenging problems in the context of industrial, medical and economical applications, where the transition from model-based numerical si- lations to model-based design and optimal control is crucial. For the treatment of such optimization problems the interaction of optimization techniques and num- ical simulation plays a central role. After proper discretization, the number of op- 3 10 timization variables varies between 10 and 10 . It is only very recently that the enormous advances in computing power have made it possible to attack problems of this size. However, in order to accomplish this task it is crucial to utilize and f- ther explore the speci?c mathematical structure of optimization problems with PDE constraints, and to develop new mathematical approaches concerning mathematical analysis, structure exploiting algorithms, and discretization, with a special focus on prototype applications. The present book provides a modern introduction to the rapidly developing ma- ematical ?eld of optimization with PDE constraints. The ?rst chapter introduces to the analytical background and optimality theory for optimization problems with PDEs. Optimization problems with PDE-constraints are posed in in?nite dim- sional spaces. Therefore, functional analytic techniques, function space theory, as well as existence- and uniqueness results for the underlying PDE are essential to study the existence of optimal solutions and to derive optimality conditions.
Download or read book Applied and Computational Optimal Control written by Kok Lay Teo and published by Springer Nature. This book was released on 2021-05-24 with total page 581 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to furnish the reader with a rigorous and detailed exposition of the concept of control parametrization and time scaling transformation. It presents computational solution techniques for a special class of constrained optimal control problems as well as applications to some practical examples. The book may be considered an extension of the 1991 monograph A Unified Computational Approach Optimal Control Problems, by K.L. Teo, C.J. Goh, and K.H. Wong. This publication discusses the development of new theory and computational methods for solving various optimal control problems numerically and in a unified fashion. To keep the book accessible and uniform, it includes those results developed by the authors, their students, and their past and present collaborators. A brief review of methods that are not covered in this exposition, is also included. Knowledge gained from this book may inspire advancement of new techniques to solve complex problems that arise in the future. This book is intended as reference for researchers in mathematics, engineering, and other sciences, graduate students and practitioners who apply optimal control methods in their work. It may be appropriate reading material for a graduate level seminar or as a text for a course in optimal control.
Download or read book A Unified Computational Approach to Optimal Control Problems written by K. L. Teo and published by . This book was released on 1991 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concerned with optimal control theory, this text aims to supplement existing work in this field from the viewpoints of computation and applications. In particular those computational algorithms derived from the concept of control parametrization are emphasized in this text.
Download or read book Practical Methods for Optimal Control and Estimation Using Nonlinear Programming written by John T. Betts and published by SIAM. This book was released on 2010-01-01 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: A focused presentation of how sparse optimization methods can be used to solve optimal control and estimation problems.
Download or read book Control of Coupled Partial Differential Equations written by Karl Kunisch and published by Springer Science & Business Media. This book was released on 2007-08-08 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains selected contributions originating from the ‘Conference on Optimal Control of Coupled Systems of Partial Differential Equations’, held at the ‘Mathematisches Forschungsinstitut Oberwolfach’ in April 2005. With their articles, leading scientists cover a broad range of topics such as controllability, feedback-control, optimality systems, model-reduction techniques, analysis and optimal control of flow problems, and fluid-structure interactions, as well as problems of shape and topology optimization. Applications affected by these findings are distributed over all time and length scales starting with optimization and control of quantum mechanical systems, the design of piezoelectric acoustic micro-mechanical devices, or optimal control of crystal growth to the control of bodies immersed into a fluid, airfoil design, and much more. The book addresses advanced students and researchers in optimization and control of infinite dimensional systems, typically represented by partial differential equations. Readers interested either in theory or in numerical simulation of such systems will find this book equally appealing.
Download or read book Challenges in Automation Robotics and Measurement Techniques written by Roman Szewczyk and published by Springer. This book was released on 2016-02-15 with total page 886 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the set of papers accepted for presentation at the International Conference Automation, held in Warsaw, 2-4 March of 2016. It presents the research results presented by top experts in the fields of industrial automation, control, robotics and measurement techniques. Each chapter presents a thorough analysis of a specific technical problem which is usually followed by numerical analysis, simulation, and description of results of implementation of the solution of a real world problem. The presented theoretical results, practical solutions and guidelines will be valuable for both researchers working in the area of engineering sciences and for practitioners solving industrial problems.
