Download or read book Optimal Control of the Sweeping Process Over Polyhedral Controlled Sets written by Giovanni Colombo and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The paper addresses a new class of optimal control problems governed by the dissipative and discontinuous differential inclusion of the sweeping/Moreau process while using controls to determine the best shape of moving convex polyhedra in order to optimize the given Bolza-type functional, which depends on control and state variables as well as their velocities. Besides the highly non-Lipschitzian nature of the unbounded differential inclusion of the controlled sweeping process, the optimal control problems under consideration contain intrinsic state constraints of the inequality and equality types. All of this creates serious challenges for deriving necessary optimality conditions. We develop here the method of discrete approximations and combine it with advanced tools of first-order and second-order variational analysis and generalized differentiation. This approach allows us to establish constructive necessary optimality conditions for local minimizers of the controlled sweeping process expressed entirely in terms of the problem data under fairly unrestrictive assumptions. As a by-product of the developed approach, we prove the strong W1;2-convergence of optimal solutions of discrete approximations to a given local minimizer of the continuous-time system and derive necessary optimality conditions for the discrete counterparts. The established necessary optimality conditions for the sweeping process are illustrated by several examples.
Download or read book Optimization of Controlled Sweeping Processes with Applications written by Nguyen-Truc-Dao Nguyen and published by . This book was released on 2021 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: The dissertation is devoted to the study of a new class of optimal control problems described by a controlled version of Moreau's sweeping process governed by convex polyhedra, where measurable control actions enter additive perturbations. This class of problems, which addresses unbounded discontinuous differential inclusions with intrinsic state constraints, is truly challenging and underinvestigated in control theory while being highly important for various applications. To attack such problems with constrained measurable controls, we develop a reƠ̐1ned method of discrete approximations with establishing its well-posedness and strong convergence. This approach, married to advanced tools of first-order and second-order variational analysis and generalized differentiation, allows us to derive adequate collections of necessary optimality conditions for local minimizers, first in discrete-time problems and then in the original continuous-time controlled sweeping process by passing to the limit. The new results include an appropriate maximum condition and significantly extend the previous ones obtained under essentially more restrictive assumptions. We compare them with other versions of the maximum principle for controlled sweeping processes that have been recently established for global minimizers in problems with smooth sweeping sets by using different techniques. Besides illustrative examples, we apply the obtained results to optimal control problems associated with the mobile robot model and traffic flow model through a doorway, which are formulated in this thesis. The derived optimality conditions allow us to develop an effective procedure to solve these problems in a general setting and completely calculate optimal solutions in particular situations.
Download or read book Recent Developments in Automatic Control Systems written by Yuriy P. Kondratenko and published by CRC Press. This book was released on 2023-01-30 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides an overview of the recent developments in modern control systems including new theoretical findings and successful examples of practical implementation of the control theory in different areas of industrial and special applications. Recent Developments in Automatic Control Systems consists of extended versions of selected papers presented at the XXVI International Conference on Automatic Control "Automation 2020" (October 13–15, 2020, Kyiv, Ukraine) which is the main Ukrainian Control Conference organized by the Ukrainian Association on Automatic Control (national member organization of IFAC) and the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute". This is the third monograph in the River Publishers series in Automation, Control and Robotics based on the selected papers of the Ukrainian Control Conferences "Automation", in particular, the first monograph Control Systems: Theory and Applications (2018) was published based on "Automation – 2017" and the second monograph Advanced Control Systems: Theory and Applications was based on "Automation – 2018". The monograph is divided into three main parts: (a) Advances in Theoretical Research of Control Systems; (b) Advances in Control Systems Application; (c) Recent Developments in Collaborative Automation. The chapters have been structured to provide an easy-to-follow introduction to the topics that are addressed, including the most relevant references, so that anyone interested in this field can get started in the area. This book may be useful for researchers and students who are interesting in recent developments in modern control systems, robust adaptive systems, optimal control, fuzzy control, motion control, identification, modelling, differential games, evolutionary optimization, reliability control, security control, intelligent robotics and cyber–physical systems.
Download or read book Variational Analysis and Generalized Differentiation II written by Boris S. Mordukhovich and published by Springer Science & Business Media. This book was released on 2006-03-02 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive and state-of-the art study of the basic concepts and principles of variational analysis and generalized differentiation in both finite-dimensional and infinite-dimensional spaces Presents numerous applications to problems in the optimization, equilibria, stability and sensitivity, control theory, economics, mechanics, etc.
Download or read book Planning Algorithms written by Steven M. LaValle and published by Cambridge University Press. This book was released on 2006-05-29 with total page 844 pages. Available in PDF, EPUB and Kindle. Book excerpt: Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. Written for computer scientists and engineers with interests in artificial intelligence, robotics, or control theory, this is the only book on this topic that tightly integrates a vast body of literature from several fields into a coherent source for teaching and reference in a wide variety of applications. Difficult mathematical material is explained through hundreds of examples and illustrations.
Download or read book Optimal Control of a Perturbed Sweeping Process with Applications to the Crowd Motion Model written by Tan Hoang Cao and published by . This book was released on 2016 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: The dissertation is devoted to the study and applications of a new class of optimal control problems governed by a perturbed sweeping process of the hysteresis type with control functions acting in both play-and-stop operator and additive perturbations. Such control problems can be reduced to optimization of discontinuous and unbounded dif- ferential inclusions with pointwise state constraints, which are immensely challenging in control theory and prevent employing conventional variation techniques to derive neces- sary optimality conditions. We develop the method of discrete approximations married with appropriate generalized differential tools of modern variational analysis to overcome principal difficulties in passing to the limit from optimality conditions for finite-difference systems. This approach leads us to nondegenerate necessary conditions for local minimiz- ers of the controlled sweeping process expressed entirely via the problem data. Besides illustrative examples, we apply the obtained results to an optimal control problem asso- ciated with of the crowd motion model of traffic flow in a corridor, which is formulated in this thesis. The derived optimality conditions allow us to develop an effective procedure to solve this problem in a general setting and completely calculate optimal solutions in particular situations.
Download or read book Algorithms for Optimization written by Mykel J. Kochenderfer and published by MIT Press. This book was released on 2019-03-12 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to optimization with a focus on practical algorithms for the design of engineering systems. This book offers a comprehensive introduction to optimization with a focus on practical algorithms. The book approaches optimization from an engineering perspective, where the objective is to design a system that optimizes a set of metrics subject to constraints. Readers will learn about computational approaches for a range of challenges, including searching high-dimensional spaces, handling problems where there are multiple competing objectives, and accommodating uncertainty in the metrics. Figures, examples, and exercises convey the intuition behind the mathematical approaches. The text provides concrete implementations in the Julia programming language. Topics covered include derivatives and their generalization to multiple dimensions; local descent and first- and second-order methods that inform local descent; stochastic methods, which introduce randomness into the optimization process; linear constrained optimization, when both the objective function and the constraints are linear; surrogate models, probabilistic surrogate models, and using probabilistic surrogate models to guide optimization; optimization under uncertainty; uncertainty propagation; expression optimization; and multidisciplinary design optimization. Appendixes offer an introduction to the Julia language, test functions for evaluating algorithm performance, and mathematical concepts used in the derivation and analysis of the optimization methods discussed in the text. The book can be used by advanced undergraduates and graduate students in mathematics, statistics, computer science, any engineering field, (including electrical engineering and aerospace engineering), and operations research, and as a reference for professionals.
Download or read book A Mathematical Introduction to Robotic Manipulation written by Richard M. Murray and published by CRC Press. This book was released on 2017-12-14 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Mathematical Introduction to Robotic Manipulation presents a mathematical formulation of the kinematics, dynamics, and control of robot manipulators. It uses an elegant set of mathematical tools that emphasizes the geometry of robot motion and allows a large class of robotic manipulation problems to be analyzed within a unified framework. The foundation of the book is a derivation of robot kinematics using the product of the exponentials formula. The authors explore the kinematics of open-chain manipulators and multifingered robot hands, present an analysis of the dynamics and control of robot systems, discuss the specification and control of internal forces and internal motions, and address the implications of the nonholonomic nature of rolling contact are addressed, as well. The wealth of information, numerous examples, and exercises make A Mathematical Introduction to Robotic Manipulation valuable as both a reference for robotics researchers and a text for students in advanced robotics courses.
Download or read book Variational Analysis and Applications written by Boris S. Mordukhovich and published by Springer. This book was released on 2018-08-02 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building on fundamental results in variational analysis, this monograph presents new and recent developments in the field as well as selected applications. Accessible to a broad spectrum of potential readers, the main material is presented in finite-dimensional spaces. Infinite-dimensional developments are discussed at the end of each chapter with comprehensive commentaries which emphasize the essence of major results, track the genesis of ideas, provide historical comments, and illuminate challenging open questions and directions for future research. The first half of the book (Chapters 1–6) gives a systematic exposition of key concepts and facts, containing basic material as well as some recent and new developments. These first chapters are particularly accessible to masters/doctoral students taking courses in modern optimization, variational analysis, applied analysis, variational inequalities, and variational methods. The reader’s development of skills will be facilitated as they work through each, or a portion of, the multitude of exercises of varying levels. Additionally, the reader may find hints and references to more difficult exercises and are encouraged to receive further inspiration from the gems in chapter commentaries. Chapters 7–10 focus on recent results and applications of variational analysis to advanced problems in modern optimization theory, including its hierarchical and multiobjective aspects, as well as microeconomics, and related areas. It will be of great use to researchers and professionals in applied and behavioral sciences and engineering.
Download or read book Simulating Humans written by Norman I. Badler and published by Oxford University Press, USA. This book was released on 1993-09-02 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: The area of simulated human figures is an active research area in computer graphics, and Norman Badler's group at the University of Pennsylvania is one of the leaders in the field. This book summarizes the state of the art in simulating human figures, discusses many of the interesting application areas, and makes some assumptions and predictions about where the field is going.
Download or read book Hybrid Systems Computation and Control written by Nancy Lynch and published by Springer Science & Business Media. This book was released on 2007-10-28 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Third International Workshop on Hybrid Systems: Computation and Control, HSCC 2000, held in Pittsburgh, PA, USA in March 2000.; The 32 revised full papers presented together with abstracts of four invited talks were carefully reviewed and selected from a total of 71 papers submitted.; The focus of the works presented is on modeling, control, synthesis, design and verification of hybrid systems.; Among the application areas covered are control of electromechanical systems, air traffic control, control of automated freeways, and chemical process control.
Download or read book Computational Optimal Transport written by Gabriel Peyre and published by Foundations and Trends(r) in M. This book was released on 2019-02-12 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of Optimal Transport (OT) is to define geometric tools that are useful to compare probability distributions. Their use dates back to 1781. Recent years have witnessed a new revolution in the spread of OT, thanks to the emergence of approximate solvers that can scale to sizes and dimensions that are relevant to data sciences. Thanks to this newfound scalability, OT is being increasingly used to unlock various problems in imaging sciences (such as color or texture processing), computer vision and graphics (for shape manipulation) or machine learning (for regression, classification and density fitting). This monograph reviews OT with a bias toward numerical methods and their applications in data sciences, and sheds lights on the theoretical properties of OT that make it particularly useful for some of these applications. Computational Optimal Transport presents an overview of the main theoretical insights that support the practical effectiveness of OT before explaining how to turn these insights into fast computational schemes. Written for readers at all levels, the authors provide descriptions of foundational theory at two-levels. Generally accessible to all readers, more advanced readers can read the specially identified more general mathematical expositions of optimal transport tailored for discrete measures. Furthermore, several chapters deal with the interplay between continuous and discrete measures, and are thus targeting a more mathematically-inclined audience. This monograph will be a valuable reference for researchers and students wishing to get a thorough understanding of Computational Optimal Transport, a mathematical gem at the interface of probability, analysis and optimization.
Download or read book Impacts in Mechanical Systems written by Bernard Brogliato and published by Springer Science & Business Media. This book was released on 2000-08-15 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume constitutes an advanced introduction to the field of analysis, modeling and numerical simulation of rigid body mechanical systems with unilateral constraints. The topics include Moreau's sweeping process, the numerical analysis of nonsmooth multibody systems with friction, the study of energetical restitution coefficients for elasto-plastic models, the study of stability and bifurcation in systems with impacts, and the development of a multiple impact rule for Newton's cradle and the simple rocking model. Combining pedagogical aspects with innovative approaches, this book will not only be of interest to researchers working actively in the field, but also to graduate students wishing to get acquainted with this field of research through lectures written at a level also accessible to nonspecialists.
Download or read book Second Order Variational Analysis in Optimization Variational Stability and Control written by Boris S. Mordukhovich and published by Springer Nature. This book was released on with total page 802 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Visualization written by H.-C. Hege and published by Springer Science & Business Media. This book was released on 1998-10-20 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Visualization is a young new discipline. It offers efficient visualization tools to the classical subjects of mathematics, and applies mathematical techniques to problems in computer graphics and scientific visualization. Originally, it started in the interdisciplinary area of differential geometry, numerical mathematics, and computer graphics. In recent years, the methods developed have found important applications. The current volume is the quintessence of an international workshop in September 1997 in Berlin, focusing on recent developments in this emerging area. Experts present selected research work on new algorithms for visualization problems, describe the application and experiments in geometry, and develop new numerical or computer graphical techniques.
Download or read book Optimization of Complex Systems Theory Models Algorithms and Applications written by Hoai An Le Thi and published by Springer. This book was released on 2019-06-15 with total page 1164 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains 112 papers selected from about 250 submissions to the 6th World Congress on Global Optimization (WCGO 2019) which takes place on July 8–10, 2019 at University of Lorraine, Metz, France. The book covers both theoretical and algorithmic aspects of Nonconvex Optimization, as well as its applications to modeling and solving decision problems in various domains. It is composed of 10 parts, each of them deals with either the theory and/or methods in a branch of optimization such as Continuous optimization, DC Programming and DCA, Discrete optimization & Network optimization, Multiobjective programming, Optimization under uncertainty, or models and optimization methods in a specific application area including Data science, Economics & Finance, Energy & Water management, Engineering systems, Transportation, Logistics, Resource allocation & Production management. The researchers and practitioners working in Nonconvex Optimization and several application areas can find here many inspiring ideas and useful tools & techniques for their works.
Download or read book Polygon Mesh Processing written by Mario Botsch and published by CRC Press. This book was released on 2010-10-07 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometry processing, or mesh processing, is a fast-growing area of research that uses concepts from applied mathematics, computer science, and engineering to design efficient algorithms for the acquisition, reconstruction, analysis, manipulation, simulation, and transmission of complex 3D models. Applications of geometry processing algorithms already cover a wide range of areas from multimedia, entertainment, and classical computer-aided design, to biomedical computing, reverse engineering, and scientific computing. Over the last several years, triangle meshes have become increasingly popular, as irregular triangle meshes have developed into a valuable alternative to traditional spline surfaces. This book discusses the whole geometry processing pipeline based on triangle meshes. The pipeline starts with data input, for example, a model acquired by 3D scanning techniques. This data can then go through processes of error removal, mesh creation, smoothing, conversion, morphing, and more. The authors detail techniques for those processes using triangle meshes. A supplemental website contains downloads and additional information.
