Download or read book A Complete Qualitative Analysis of Controllability for Planar Time invariant Bilinear Systems of Ordinary Differential Equations with Scalar Control written by Eric Anthony Remaley and published by . This book was released on 2002 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dissertation Abstracts International written by and published by . This book was released on 2003 with total page 860 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bilinear Control Systems written by David Elliott and published by Springer Science & Business Media. This book was released on 2009-09-01 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mathematical theory of control became a ?eld of study half a century ago in attempts to clarify and organize some challenging practical problems and the methods used to solve them. It is known for the breadth of the mathematics it uses and its cross-disciplinary vigor. Its literature, which can befoundinSection93ofMathematicalReviews,wasatonetimedominatedby the theory of linear control systems, which mathematically are described by linear di?erential equations forced by additive control inputs. That theory led to well-regarded numerical and symbolic computational packages for control analysis and design. Nonlinear control problems are also important; in these either the - derlying dynamical system is nonlinear or the controls are applied in a n- additiveway.Thelastfourdecadeshaveseenthedevelopmentoftheoretical work on nonlinear control problems based on di?erential manifold theory, nonlinear analysis, and several other mathematical disciplines. Many of the problems that had been solved in linear control theory, plus others that are new and distinctly nonlinear, have been addressed; some resulting general de?nitions and theorems are adapted in this book to the bilinear case.
Download or read book Stability and Control of Linear Systems written by Andrea Bacciotti and published by Springer. This book was released on 2018-11-02 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced textbook introduces the main concepts and advances in systems and control theory, and highlights the importance of geometric ideas in the context of possible extensions to the more recent developments in nonlinear systems theory. Although inspired by engineering applications, the content is presented within a strong theoretical framework and with a solid mathematical background, and the reference models are always finite dimensional, time-invariant multivariable linear systems. The book focuses on the time domain approach, but also considers the frequency domain approach, discussing the relationship between the two approaches, especially for single-input-single-output systems. It includes topics not usually addressed in similar books, such as a comparison between the frequency domain and the time domain approaches, bounded input bounded output stability (including a characterization in terms of canonical decomposition), and static output feedback stabilization for which a simple and original criterion in terms of generalized inverse matrices is proposed. The book is an ideal learning resource for graduate students of control theory and automatic control courses in engineering and mathematics, as well as a reference or self-study guide for engineers and applied mathematicians.
Download or read book Representation and Control of Infinite Dimensional Systems written by Alain Bensoussan and published by Springer Science & Business Media. This book was released on 2007-04-05 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unified, revised second edition of a two-volume set is a self-contained account of quadratic cost optimal control for a large class of infinite-dimensional systems. The original editions received outstanding reviews, yet this new edition is more concise and self-contained. New material has been added to reflect the growth in the field over the past decade. There is a unique chapter on semigroup theory of linear operators that brings together advanced concepts and techniques which are usually treated independently. The material on delay systems and structural operators has not yet appeared anywhere in book form.
Download or read book Controllability Stabilization and the Regulator Problem for Random Differential Systems written by Russell Johnson and published by American Mathematical Soc.. This book was released on 1998 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume develops a systematic study of time-dependent control processes. The basic problem of null controllability of linear systems is first considered. Using methods of ergodic theory and topological dynamics, general local null controllability criteria are given. Then the subtle question of global null controllability is studied. Next, the random linear feedback and stabilization problem is posed and solved. Using concepts of exponential dichotomy and rotation number for linear Hamiltonian systems, a solution of the Riccati equation is obtained which has extremely good robustness properties and which also preserves all the smoothness and recurrence properties of the coefficients. Finally, a general version of the local nonlinear feedback stabilization problem is solved.
Download or read book Controllability of Singularly Perturbed Linear Time Delay Systems written by Valery Y. Glizer and published by Springer Nature. This book was released on 2021-03-24 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a comprehensive analysis of the control of singularly perturbed time delay systems. Expanding on the author’s previous work on controllability of linear systems with delays in the state and control variables, this volume’s comprehensive coverage makes it a valuable addition to the field. Each chapter is self-contained, allowing readers to study them independently or in succession. After a brief introduction, the book systematically examines properties of different classes of singularly perturbed time delay systems, including linear time-dependent systems with multiple point-wise and distributed state delays. The author then considers more general singularly perturbed systems with state and control delays. Euclidean space controllability for all of these systems is also discussed, using numerous examples from real-life models throughout the text to illustrate the results presented. More technically complicated proofs are presented in separate subsections. The final chapter includes a section dedicated to non-linear time delay systems. This book is ideal for researchers, engineers, and graduate students in systems science and control theory. Other applied mathematicians and researchers working in biology and medicine will also find this volume to be a valuable resource.
Download or read book American Doctoral Dissertations written by and published by . This book was released on 2002 with total page 776 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fractional Order Systems Control Theory and Applications written by Omar Naifar and published by Springer Nature. This book was released on 2021-08-30 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to bring together the latest innovative knowledge, analysis, and synthesis of fractional control problems of nonlinear systems as well as some related applications. Fractional order systems (FOS) are dynamical systems that can be modelled by a fractional differential equation carried with a non-integer derivative. In the last few decades, the growth of science and engineering systems has considerably stimulated the employment of fractional calculus in many subjects of control theory, for example, in stability, stabilization, controllability, observability, observer design, and fault estimation. The application of control theory in FOS is an important issue in many engineering applications. So, to accurately describe these systems, the fractional order differential equations have been introduced.
Download or read book Linear Parameter Varying and Time Delay Systems written by Corentin Briat and published by Springer. This book was released on 2014-09-03 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the analysis and control of Linear Parameter-Varying Systems and Time-Delay Systems and their interactions. The purpose is to give the readers some fundamental theoretical background on these topics and to give more insights on the possible applications of these theories. This self-contained monograph is written in an accessible way for readers ranging from undergraduate/PhD students to engineers and researchers willing to know more about the fields of time-delay systems, parameter-varying systems, robust analysis, robust control, gain-scheduling techniques in the LPV fashion and LMI based approaches. The only prerequisites are basic knowledge in linear algebra, ordinary differential equations and (linear) dynamical systems. Most of the results are proved unless the proof is too complex or not necessary for a good understanding of the results. In the latter cases, suitable references are systematically provided. The first part pertains on the representation, analysis and control of LPV systems along with a reminder on robust analysis and control techniques. The second part is concerned with the representation and analysis of time-delay systems using various time-domain techniques. The third and last part is devoted to the representation, analysis, observation, filtering and control of LPV time-delay systems. The book also presents many important basic and advanced results on the manipulation of LMIs.
Download or read book The Dynamics of Control written by Fritz Colonius and published by Springer Science & Business Media. This book was released on 2000-04-20 with total page 654 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new text/reference is an excellent resource for the foundations and applications of control theory and nonlinear dynamics. All graduates, practitioners, and professionals in control theory, dynamical systems, perturbation theory, engineering, physics and nonlinear dynamics will find the book a rich source of ideas, methods and applications. With its careful use of examples and detailed development, it is suitable for use as a self-study/reference guide for all scientists and engineers.
Download or read book Bilinear Controllability Applied to a Geometric Variant of the Holding Problem written by Lester Frank Ludwig and published by . This book was released on 1980 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Controllability and Minimum Energy Control written by Jerzy Klamka and published by Springer. This book was released on 2018-06-01 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book offers a comprehensive overview of controllability problems and minimum energy control for broad classes of dynamical systems, including linear, semilinear and nonlinear systems, which are important for modeling systems in automatic control, electrical engineering, mechanics and informatics. It develops the theory of controllability for both finite and infinite dimensional dynamical systems described by differential state equation, and studies in detail functional analysis and matrix algebra, which provide essential and effective tools for the new solutions of a number of important controllability problems. The theoretical results are illustrated by examples throughout the book. Primarily intended for academic researchers working in mathematical control theory, the self-contained text is easily accessible and particularly interesting for control engineering and applied mathematics graduates.
Download or read book Continuous Time Dynamical Systems written by B.M. Mohan and published by CRC Press. This book was released on 2018-10-08 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal control deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved. An optimal control is a set of differential equations describing the paths of the control variables that minimize the cost functional. This book, Continuous Time Dynamical Systems: State Estimation and Optimal Control with Orthogonal Functions, considers different classes of systems with quadratic performance criteria. It then attempts to find the optimal control law for each class of systems using orthogonal functions that can optimize the given performance criteria. Illustrated throughout with detailed examples, the book covers topics including: Block-pulse functions and shifted Legendre polynomials State estimation of linear time-invariant systems Linear optimal control systems incorporating observers Optimal control of systems described by integro-differential equations Linear-quadratic-Gaussian control Optimal control of singular systems Optimal control of time-delay systems with and without reverse time terms Optimal control of second-order nonlinear systems Hierarchical control of linear time-invariant and time-varying systems
Download or read book Time Optimal Control of Evolution Equations written by Gengsheng Wang and published by Springer. This book was released on 2018-08-22 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph develops a framework for time-optimal control problems, focusing on minimal and maximal time-optimal controls for linear-controlled evolution equations. Its use in optimal control provides a welcome update to Fattorini’s work on time-optimal and norm-optimal control problems. By discussing the best way of representing various control problems and equivalence among them, this systematic study gives readers the tools they need to solve practical problems in control. After introducing preliminaries in functional analysis, evolution equations, and controllability and observability estimates, the authors present their time-optimal control framework, which consists of four elements: a controlled system, a control constraint set, a starting set, and an ending set. From there, they use their framework to address areas of recent development in time-optimal control, including the existence of admissible controls and optimal controls, Pontryagin’s maximum principle for optimal controls, the equivalence of different optimal control problems, and bang-bang properties. This monograph will appeal to researchers and graduate students in time-optimal control theory, as well as related areas of controllability and dynamic programming. For ease of reference, the text itself is self-contained on the topic of time-optimal control. Frequent examples throughout clarify the applications of theorems and definitions, although experience with functional analysis and differential equations will be useful.
Download or read book Planar Dynamical Systems written by Yirong Liu and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-10-29 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 2008, November 23-28, the workshop of ”Classical Problems on Planar Polynomial Vector Fields ” was held in the Banff International Research Station, Canada. Called "classical problems", it was concerned with the following: (1) Problems on integrability of planar polynomial vector fields. (2) The problem of the center stated by Poincaré for real polynomial differential systems, which asks us to recognize when a planar vector field defined by polynomials of degree at most n possesses a singularity which is a center. (3) Global geometry of specific classes of planar polynomial vector fields. (4) Hilbert’s 16th problem. These problems had been posed more than 110 years ago. Therefore, they are called "classical problems" in the studies of the theory of dynamical systems. The qualitative theory and stability theory of differential equations, created by Poincaré and Lyapunov at the end of the 19th century, had major developments as two branches of the theory of dynamical systems during the 20th century. As a part of the basic theory of nonlinear science, it is one of the very active areas in the new millennium. This book presents in an elementary way the recent significant developments in the qualitative theory of planar dynamical systems. The subjects are covered as follows: the studies of center and isochronous center problems, multiple Hopf bifurcations and local and global bifurcations of the equivariant planar vector fields which concern with Hilbert’s 16th problem. The book is intended for graduate students, post-doctors and researchers in dynamical systems. For all engineers who are interested in the theory of dynamical systems, it is also a reasonable reference. It requires a minimum background of a one-year course on nonlinear differential equations.
Download or read book Control and Nonlinearity written by Jean-Michel Coron and published by American Mathematical Soc.. This book was released on 2007 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents methods to study the controllability and the stabilization of nonlinear control systems in finite and infinite dimensions. The emphasis is put on specific phenomena due to nonlinearities. In particular, many examples are given where nonlinearities turn out to be essential to get controllability or stabilization. Various methods are presented to study the controllability or to construct stabilizing feedback laws. The power of these methods is illustrated by numerous examples coming from such areas as celestial mechanics, fluid mechanics, and quantum mechanics. The book is addressed to graduate students in mathematics or control theory, and to mathematicians or engineers with an interest in nonlinear control systems governed by ordinary or partial differential equations.
