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Presents and demonstrates stabilizer design techniques that can be used to solve stabilization problems with constraints. These methods have their origins in convex programming and stability theory. However, to provide a practical capability in stabilizer design, the methods are tailored to the special features and needs of this field. Hence, the main emphasis of this book is on the methods of stabilization, rather than optimization and stability theory. The text is divided into three parts. Part I contains some background material. Part II is devoted to behavior of control systems, taking examples from mechanics to illustrate the theory. Finally, Part III deals with nonlocal stabilization problems, including a study of the global stabilization problem.
Presents and demonstrates stabilizer design techniques that can be used to solve stabilization problems with constraints. These methods have their origins in convex programming and stability theory. However, to provide a practical capability in stabilizer design, the methods are tailored to the special features and needs of this field. Hence, the main emphasis of this book is on the methods of stabilization, rather than optimization and stability theory. The text is divided into three parts. Part I contains some background material. Part II is devoted to behavior of control systems, taking examples from mechanics to illustrate the theory. Finally, Part III deals with nonlocal stabilization problems, including a study of the global stabilization problem.
The first optimal design problem for an elastic column subject to buckling was formulated by Lagrange over 200 years ago. However, rapid development of structural optimization under stability constraints occurred only in the last twenty years. In numerous optimal structural design problems the stability phenomenon becomes one of the most important factors, particularly for slender and thin-walled elements of aerospace structures, ships, precision machines, tall buildings etc. In engineering practice stability constraints appear more often than it might be expected; even when designing a simple beam of constant width and variable depth, the width - if regarded as a design variable - is finally determined by a stability constraint (lateral stability). Mathematically, optimal structural design under stability constraints usually leads to optimization with respect to eigenvalues, but some cases fall even beyond this type of problems. A total of over 70 books has been devoted to structural optimization as yet, but none of them has treated stability constraints in a sufficiently broad and comprehensive manner. The purpose of the present book is to fill this gap. The contents include a discussion of the basic structural stability and structural optimization problems and the pertinent solution methods, followed by a systematic review of solutions obtained for columns, arches, bar systems, plates, shells and thin-walled bars. A unified approach based on Pontryagin's maximum principle is employed inasmuch as possible, at least to problems of columns, arches and plates. Parametric optimization is discussed as well.
Unifying two decades of research, this book is the first to establish a comprehensive foundation for a systematic analysis and design of linear systems with general state and input constraints. For such systems, which can be used as models for most nonlinear systems, the issues of stability, controller design, additonal constraints, and satisfactory performance are addressed. The book is an excellent reference for practicing engineers, graduate students, and researchers in control systems theory and design. It may also serve as an advanced graduate text for a course or a seminar in nonlinear control systems theory and design in applied mathematics or engineering departments. Minimal prerequisites include a first graduate course in state-space methods as well as a first course in control systems design.
Stability-Constrained Optimization for Modern Power System Operation and Planning Comprehensive treatment of an aspect of stability constrained operations and planning, including the latest research and engineering practices Stability-Constrained Optimization for Modern Power System Operation and Planning focuses on the subject of power system stability. Unlike other books in this field, which focus mainly on the dynamic modeling, stability analysis, and controller design for power systems, this book is instead dedicated to stability-constrained optimization methodologies for power system stability enhancement, including transient stability-constrained power system dispatch and operational control, and voltage stability-constrained dynamic VAR Resources planning in the power grid. Authored by experts with established track records in both research and industry, Stability-Constrained Optimization for Modern Power System Operation and Planning covers three parts: Overview of power system stability, including definition, classification, phenomenon, mathematical models and analysis tools for stability assessment, as well as a review of recent large-scale blackouts in the world Transient stability-constrained optimal power flow (TSC-OPF) and transient stability constrained-unit commitment (TSC-UC) for power system dispatch and operational control, including a series of optimization model formulations, transient stability constraint construction and extraction methods, and efficient solution approaches Optimal planning of dynamic VAR Resources (such as STATCOM and SVC) in power system for voltage stability enhancement, including a set of voltage stability indices, candidate bus selection methods, multi-objective optimization model formulations, and high-quality solution approaches Stability-Constrained Optimization for Modern Power System Operation and Planning provides the latest research findings to scholars, researchers, and postgraduate students who are seeking optimization methodologies for power system stability enhancement, while also offering key practical methods to power system operators, planners, and optimization algorithm developers in the power industry.
While the stability theory for systems with bilateral constraints is a well-established field, this monograph represents a systematic study of mechanical systems with unilateral constraints, such as unilateral contact, impact and friction. Such unilateral constraints give rise to non-smooth dynamical models for which stability theory is developed in this work. The book will be of interest to those working in the field of non-smooth mechanics and dynamics.
​Stochastic Control and Filtering over Constrained Communication Networks presents up-to-date research developments and novel methodologies on stochastic control and filtering for networked systems under constrained communication networks. It provides a framework of optimal controller/filter design, resilient filter design, stability and performance analysis for the systems considered, subject to various kinds of communication constraints, including signal-to-noise constraints, bandwidth constraints, and packet drops. Several techniques are employed to develop the controllers and filters desired, including: recursive Riccati equations; matrix decomposition; optimal estimation theory; and mathematical optimization methods. Readers will benefit from the book’s new concepts, models and methodologies that have practical significance in control engineering and signal processing. Stochastic Control and Filtering over Constrained Communication Networks is a practical research reference for engineers dealing with networked control and filtering problems. It is also of interest to academics and students working in control and communication networks.
A number of methods currently exist for the analysis and design of slopes. This book provides a critical review of these and offers several more appropriate approaches for overcoming numerical convergence and the location of critical failure surfaces in two-dimensional and three-dimensional cases. New concepts in three-dimensional stability analysis, finite element analysis and the extension of slope stability problems to lateral earth pressure problems are also addressed. It gives helpful practical advice and design resources in the form of recommendations for good analysis and design practice, design charts and tables for the engineer. Limitations are detailed of both limit equilibrium and the finite element method in the assessment of the stability of a slope, and guidance is provided for assessing the fundamental assumptions and limitations of stability analysis methods and computer modelling. The book provides ample examples to illustrate how this range of problems should be dealt with. The final chapter touches on design and its implementation on site. The emphasis is on the transfer of the design to its physical implementation on site in a holistic way, taking full account of the latest developments in construction technology. Engineering and construction problems tend to be pigeonholed into different classes of problem such as slope stability, bearing capacity and earth pressure behind retaining structures. This is quite unnecessary. This book offers a unified approach, which is conceptually, practically and philosophically more satisfying.
Optimization problems subject to constraints governed by partial differential equations (PDEs) are among the most challenging problems in the context of industrial, economical and medical applications. Almost the entire range of problems in this field of research was studied and further explored as part of the Deutsche Forschungsgemeinschaft (DFG) priority program 1253 on “Optimization with Partial Differential Equations” from 2006 to 2013. The investigations were motivated by the fascinating potential applications and challenging mathematical problems that arise in the field of PDE constrained optimization. New analytic and algorithmic paradigms have been developed, implemented and validated in the context of real-world applications. In this special volume, contributions from more than fifteen German universities combine the results of this interdisciplinary program with a focus on applied mathematics. The book is divided into five sections on “Constrained Optimization, Identification and Control”, “Shape and Topology Optimization”, “Adaptivity and Model Reduction”, “Discretization: Concepts and Analysis” and “Applications”. Peer-reviewed research articles present the most recent results in the field of PDE constrained optimization and control problems. Informative survey articles give an overview of topics that set sustainable trends for future research. This makes this special volume interesting not only for mathematicians, but also for engineers and for natural and medical scientists working on processes that can be modeled by PDEs.
Optimal design of structures leads, as a rule, to slender and thin-walled shapes of the elements, and such elements are subject to the loss of stability. Hence the constraints of structural optimization usually include stability constraints, expressed by some eigenvalues. Optimal design under vibration constraints belongs also to optimization with respect to eigenvalues. The present volume gives a short introduction to structural optimization and then pays particular attention to multimodal optimization under stability and vibration constraints, both in elastic and inelastic range. One part is devoted to thin-walled bars optimized for interactive buckling with imperfections taken into account. The volume is of interest both to researchers and design engineers: it covers the most recent results of multimodal and interactive optimization, allowing for inelastic behaviour of structures, and the constraints discussed appear in almost all problems of engineering design.