Download or read book Constrained Optimization of Linear Systems for Infinite Horizon Problems written by Charles Roger Glassey and published by . This book was released on 1965 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some methods of optimal control theory are extended with a view toward applications to production and inventory control. A linear, discrete time, deterministic system with vector state and decision variables is optimized relative to a quadratic criterion. The optimal control is shown to be piecewise linear in the state vector when the decision is constrained to be nonnegative, and an algorithm is presented for computing optimal controls. The following results are obtained for the infinite horizon unconstrained problem with no discounting of future costs: (1) necessary conditions for convergence of optimal N-period policies. (2) optimal properties of this limit policy. These results are applied to modify the finite horizon algorithm to obtain optimal controls for the infinite horizon constrained problem. Results of some computations are presented. (Author).

Download or read book The Linearization Method for Constrained Optimization written by Boris N. Pshenichnyj and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: Techniques of optimization are applied in many problems in economics, automatic control, engineering, etc. and a wealth of literature is devoted to this subject. The first computer applications involved linear programming problems with simp- le structure and comparatively uncomplicated nonlinear pro- blems: These could be solved readily with the computational power of existing machines, more than 20 years ago. Problems of increasing size and nonlinear complexity made it necessa- ry to develop a complete new arsenal of methods for obtai- ning numerical results in a reasonable time. The lineariza- tion method is one of the fruits of this research of the last 20 years. It is closely related to Newton's method for solving systems of linear equations, to penalty function me- thods and to methods of nondifferentiable optimization. It requires the efficient solution of quadratic programming problems and this leads to a connection with conjugate gra- dient methods and variable metrics. This book, written by one of the leading specialists of optimization theory, sets out to provide - for a wide readership including engineers, economists and optimization specialists, from graduate student level on - a brief yet quite complete exposition of this most effective method of solution of optimization problems.

Download or read book Infinite Horizon Optimal Control written by Dean A. Carlson and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph deals with various classes of deterministic continuous time optimal control problems wh ich are defined over unbounded time intervala. For these problems, the performance criterion is described by an improper integral and it is possible that, when evaluated at a given admissible element, this criterion is unbounded. To cope with this divergence new optimality concepts; referred to here as "overtaking", "weakly overtaking", "agreeable plans", etc. ; have been proposed. The motivation for studying these problems arisee primarily from the economic and biological aciences where models of this nature arise quite naturally since no natural bound can be placed on the time horizon when one considers the evolution of the state of a given economy or species. The reeponsibility for the introduction of this interesting class of problems rests with the economiste who first studied them in the modeling of capital accumulation processes. Perhaps the earliest of these was F. Ramsey who, in his seminal work on a theory of saving in 1928, considered a dynamic optimization model defined on an infinite time horizon. Briefly, this problem can be described as a "Lagrange problem with unbounded time interval". The advent of modern control theory, particularly the formulation of the famoue Maximum Principle of Pontryagin, has had a considerable impact on the treatment of these models as well as optimization theory in general.

Download or read book Feedback Systems written by Karl Johan Åström and published by Princeton University Press. This book was released on 2021-02-02 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The essential introduction to the principles and applications of feedback systems—now fully revised and expanded This textbook covers the mathematics needed to model, analyze, and design feedback systems. Now more user-friendly than ever, this revised and expanded edition of Feedback Systems is a one-volume resource for students and researchers in mathematics and engineering. It has applications across a range of disciplines that utilize feedback in physical, biological, information, and economic systems. Karl Åström and Richard Murray use techniques from physics, computer science, and operations research to introduce control-oriented modeling. They begin with state space tools for analysis and design, including stability of solutions, Lyapunov functions, reachability, state feedback observability, and estimators. The matrix exponential plays a central role in the analysis of linear control systems, allowing a concise development of many of the key concepts for this class of models. Åström and Murray then develop and explain tools in the frequency domain, including transfer functions, Nyquist analysis, PID control, frequency domain design, and robustness. Features a new chapter on design principles and tools, illustrating the types of problems that can be solved using feedback Includes a new chapter on fundamental limits and new material on the Routh-Hurwitz criterion and root locus plots Provides exercises at the end of every chapter Comes with an electronic solutions manual An ideal textbook for undergraduate and graduate students Indispensable for researchers seeking a self-contained resource on control theory

Download or read book Constrained Optimal Control of Linear and Hybrid Systems written by Francesco Borrelli and published by Springer. This book was released on 2003-09-04 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many practical control problems are dominated by characteristics such as state, input and operational constraints, alternations between different operating regimes, and the interaction of continuous-time and discrete event systems. At present no methodology is available to design controllers in a systematic manner for such systems. This book introduces a new design theory for controllers for such constrained and switching dynamical systems and leads to algorithms that systematically solve control synthesis problems. The first part is a self-contained introduction to multiparametric programming, which is the main technique used to study and compute state feedback optimal control laws. The book's main objective is to derive properties of the state feedback solution, as well as to obtain algorithms to compute it efficiently. The focus is on constrained linear systems and constrained linear hybrid systems. The applicability of the theory is demonstrated through two experimental case studies: a mechanical laboratory process and a traction control system developed jointly with the Ford Motor Company in Michigan.

Download or read book Technical Abstract Bulletin written by and published by . This book was released on with total page 908 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book An Approximation Framework for Infinite Horizon Optimization Problems in a Mathematical Programming Setting written by International Business Machines Corporation. Research Division and published by . This book was released on 1999 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "Dynamic optimization problems, including optimal control problems, have typically relied on the solution techniques of dynamic programming, involving the sequential solution of certain optimality equations. However, many problems cannot be handled this way, due to complex constraints, a continuous state space, and other complicating factors. When recast as mathematical programs relying on the powerful tools of optimization, especially duality, and decomposability to deal with very large problems, the boundaries imposed by dynamic programming are lifted. This paper develops approximation techniques for stationary infinite horizon problems with discounted costs, in the framework of mathematical programming. A reference is given for parallel results for stochastic dynamic optimization problems."

Download or read book Linear Semi Infinite Optimization written by Miguel A. Goberna and published by . This book was released on 1998-03-11 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: A linear semi-infinite program is an optimization problem with linear objective functions and linear constraints in which either the number of unknowns or the number of constraints is finite. The many direct applications of linear semi-infinite optimization (or programming) have prompted considerable and increasing research effort in recent years. The authors' aim is to communicate the main theoretical ideas and applications techniques of this fascinating area, from the perspective of convex analysis. The four sections of the book cover: * Modelling with primal and dual problems - the primal problem, space of dual variables, the dual problem. * Linear semi-infinite systems - existence theorems, alternative theorems, redundancy phenomena, geometrical properties of the solution set. * Theory of linear semi-infinite programming - optimality, duality, boundedness, perturbations, well-posedness. * Methods of linear semi-infinite programming - an overview of the main numerical methods for primal and dual problems. Exercises and examples are provided to illustrate both theory and applications. The reader is assumed to be familiar with elementary calculus, linear algebra and general topology. An appendix on convex analysis is provided to ensure that the book is self-contained. Graduate students and researchers wishing to gain a deeper understanding of the main ideas behind the theory of linear optimization will find this book to be an essential text.

Download or read book Linear Optimal Control Systems written by Huibert Kwakernaak and published by Wiley-Interscience. This book was released on 1972-11-10 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book attempts to reconcile modern linear control theory with classical control theory. One of the major concerns of this text is to present design methods, employing modern techniques, for obtaining control systems that stand up to the requirements that have been so well developed in the classical expositions of control theory. Therefore, among other things, an entire chapter is devoted to a description of the analysis of control systems, mostly following the classical lines of thought. In the later chapters of the book, in which modern synthesis methods are developed, the chapter on analysis is recurrently referred to. Furthermore, special attention is paid to subjects that are standard in classical control theory but are frequently overlooked in modern treatments, such as nonzero set point control systems, tracking systems, and control systems that have to cope with constant disturbances. Also, heavy emphasis is placed upon the stochastic nature of control problems because the stochastic aspects are so essential." --Preface.

Download or read book Theory And Practice Of Control And Systems Proceedings Of The 6th Ieee Mediterranean Conference written by Antonio Tornambe and published by World Scientific. This book was released on 1999-01-04 with total page 863 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gathers together all the lectures presented at the 6th IEEE Mediterranean Conference. It focuses on the mathematical aspects in the theory and practice of control and systems, including stability and stabilizability, robust control, adaptive control, robotics and manufacturing; these topics are under intense investigation and development in the engineering and mathematics communities. The volume should have immediate appeal for a large group of engineers and mathematicians who are interested in very abstract as well as very concrete aspects of control and system theory.

Download or read book Directions in Mathematical Systems Theory and Optimization written by Anders Rantzer and published by Springer. This book was released on 2003-07-01 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: For more than three decades, Anders Lindquist has delivered fundamental cont- butions to the ?elds of systems, signals and control. Throughout this period, four themes can perhaps characterize his interests: Modeling, estimation and ?ltering, feedback and robust control. His contributions to modeling include seminal work on the role of splitting subspaces in stochastic realization theory, on the partial realization problem for both deterministic and stochastic systems, on the solution of the rational covariance extension problem and on system identi?cation. His contributions to ?ltering and estimation include the development of fast ?ltering algorithms, leading to a nonlinear dynamical system which computes spectral factors in its steady state, and which provide an alternate, linear in the dimension of the state space, to computing the Kalman gain from a matrix Riccati equation. His further research on the phase portrait of this dynamical system gave a better understanding of when the Kalman ?lter will converge, answering an open question raised by Kalman. While still a student he established the separation principle for stochastic function differential equations, including some fundamental work on optimal control for stochastic systems with time lags. He continued his interest in feedback control by deriving optimal and robust control feedback laws for suppressing the effects of harmonic disturbances. Moreover, his recent work on a complete parameterization of all rational solutions to the Nevanlinna-Pick problem is providing a new approach to robust control design.

Download or read book Constrained Optimization and Lagrange Multiplier Methods written by Dimitri P. Bertsekas and published by Academic Press. This book was released on 2014-05-10 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer Science and Applied Mathematics: Constrained Optimization and Lagrange Multiplier Methods focuses on the advancements in the applications of the Lagrange multiplier methods for constrained minimization. The publication first offers information on the method of multipliers for equality constrained problems and the method of multipliers for inequality constrained and nondifferentiable optimization problems. Discussions focus on approximation procedures for nondifferentiable and ill-conditioned optimization problems; asymptotically exact minimization in the methods of multipliers; duality framework for the method of multipliers; and the quadratic penalty function method. The text then examines exact penalty methods, including nondifferentiable exact penalty functions; linearization algorithms based on nondifferentiable exact penalty functions; differentiable exact penalty functions; and local and global convergence of Lagrangian methods. The book ponders on the nonquadratic penalty functions of convex programming. Topics include large scale separable integer programming problems and the exponential method of multipliers; classes of penalty functions and corresponding methods of multipliers; and convergence analysis of multiplier methods. The text is a valuable reference for mathematicians and researchers interested in the Lagrange multiplier methods.

Download or read book Infinite Horizon Optimal Control in the Discrete Time Framework written by Joël Blot and published by Springer Science & Business Media. This book was released on 2013-11-08 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: ​​​​In this book the authors take a rigorous look at the infinite-horizon discrete-time optimal control theory from the viewpoint of Pontryagin’s principles. Several Pontryagin principles are described which govern systems and various criteria which define the notions of optimality, along with a detailed analysis of how each Pontryagin principle relate to each other. The Pontryagin principle is examined in a stochastic setting and results are given which generalize Pontryagin’s principles to multi-criteria problems. ​Infinite-Horizon Optimal Control in the Discrete-Time Framework is aimed toward researchers and PhD students in various scientific fields such as mathematics, applied mathematics, economics, management, sustainable development (such as, of fisheries and of forests), and Bio-medical sciences who are drawn to infinite-horizon discrete-time optimal control problems.

Download or read book Constrained Markov Decision Processes written by Eitan Altman and published by Routledge. This book was released on 2021-12-17 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a unified approach for the study of constrained Markov decision processes with a finite state space and unbounded costs. Unlike the single controller case considered in many other books, the author considers a single controller with several objectives, such as minimizing delays and loss, probabilities, and maximization of throughputs. It is desirable to design a controller that minimizes one cost objective, subject to inequality constraints on other cost objectives. This framework describes dynamic decision problems arising frequently in many engineering fields. A thorough overview of these applications is presented in the introduction. The book is then divided into three sections that build upon each other.

Download or read book Model Predictive Control written by Carlos Bordons Alba and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of "Model Predictive Control" provides a thorough introduction to theoretical and practical aspects of the most commonly used MPC strategies. It bridges the gap between the powerful but often abstract techniques of control researchers and the more empirical approach of practitioners. The book demonstrates that a powerful technique does not always require complex control algorithms. Many new exercises and examples have also been added throughout. Solutions available for download from the authors' website save the tutor time and enable the student to follow results more closely even when the tutor isn't present.

Download or read book Dynamics and Control of Chemical Reactors Distillation Columns and Batch Processes DYCORD 95 written by J.B. Rawlings and published by Elsevier. This book was released on 2014-05-23 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Three important areas of process dynamics and control: chemical reactors, distillation columns and batch processes are the main topics of discussion and evaluation at the IFAC Symposium on Dynamics and Control of Chemical Reactors, Distillation Columns and Batch Processes (DYCORD '95). This valuable publication was produced from the latest in the series, providing a detailed assessment of developments of key technologies within the field of process dynamics and control.

Download or read book Robotics written by Hugh Durrant-Whyte and published by MIT Press. This book was released on 2012-06-29 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers from a flagship conference reflect the latest developments in the field, including work in such rapidly advancing areas as human-robot interaction and formal methods. Robotics: Science and Systems VII spans a wide spectrum of robotics, bringing together researchers working on the algorithmic or mathematical foundations of robotics, robotics applications, and analysis of robotics systems. This volume presents the proceedings of the seventh annual Robotics: Science and Systems conference, held in 2011 at the University of Southern California. The papers presented cover a wide range of topics in robotics, spanning mechanisms, kinematics, dynamics and control, human-robot interaction and human-centered systems, distributed systems, mobile systems and mobility, manipulation, field robotics, medical robotics, biological robotics, robot perception, and estimation and learning in robotic systems. The conference and its proceedings reflect not only the tremendous growth of robotics as a discipline but also the desire in the robotics community for a flagship event at which the best of the research in the field can be presented.