Infinite Horizon Optimal Control
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Infinite Horizon Optimal Control
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Author : Dean Carlson
language : en
Publisher:
Release Date : 2014-01-15
Infinite Horizon Optimal Control written by Dean Carlson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Infinite Horizon Optimal Control
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Author : Dean A. Carlson
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Infinite Horizon Optimal Control written by Dean A. Carlson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Business & Economics categories.
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.
Infinite Horizon Optimal Control In The Discrete Time Framework
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Author : Joël Blot
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-08
Infinite Horizon Optimal Control In The Discrete Time Framework written by Joël Blot and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-08 with Mathematics categories.
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.
Infinite Horizon Optimal Control
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Author : Dean Carlson
language : en
Publisher: Springer
Release Date : 1991-10-17
Infinite Horizon Optimal Control written by Dean Carlson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-10-17 with Business & Economics categories.
This monograph deals with various classes of deterministic and stochastic continuous time optimal control problems that are defined over unbounded time intervals. 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 optimality, weakly overtaking optimality, agreeable plans, etc. , have been proposed. The motivation for studying these problems arises primarily from the economic and biological sciences where models of this type arise naturally. Indeed, any bound placed on the time hori zon is artificial when one considers the evolution of the state of an economy or species. The responsibility for the introduction of this interesting class of problems rests with the economists who first studied them in the modeling of capital accumulation processes. Perhaps the earliest of these was F. Ramsey [152] who, in his seminal work on the 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 famous Maximum Principle of Pontryagin, has had a considerable impact on the treat ment of these models as well as optimization theory in general.
Turnpike Phenomenon And Infinite Horizon Optimal Control
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Author : Alexander J. Zaslavski
language : en
Publisher: Springer
Release Date : 2014-09-04
Turnpike Phenomenon And Infinite Horizon Optimal Control written by Alexander J. Zaslavski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-04 with Mathematics categories.
This book is devoted to the study of the turnpike phenomenon and describes the existence of solutions for a large variety of infinite horizon optimal control classes of problems. Chapter 1 provides introductory material on turnpike properties. Chapter 2 studies the turnpike phenomenon for discrete-time optimal control problems. The turnpike properties of autonomous problems with extended-value integrands are studied in Chapter 3. Chapter 4 focuses on large classes of infinite horizon optimal control problems without convexity (concavity) assumptions. In Chapter 5, the turnpike results for a class of dynamic discrete-time two-player zero-sum game are proven. This thorough exposition will be very useful for mathematicians working in the fields of optimal control, the calculus of variations, applied functional analysis and infinite horizon optimization. It may also be used as a primary text in a graduate course in optimal control or as supplementary text for a variety of courses in other disciplines. Researchers in other fields such as economics and game theory, where turnpike properties are well known, will also find this Work valuable.
Stochastic Linear Quadratic Optimal Control Theory Open Loop And Closed Loop Solutions
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Author : Jingrui Sun
language : en
Publisher: Springer Nature
Release Date : 2020-06-29
Stochastic Linear Quadratic Optimal Control Theory Open Loop And Closed Loop Solutions written by Jingrui Sun and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-29 with Mathematics categories.
This book gathers the most essential results, including recent ones, on linear-quadratic optimal control problems, which represent an important aspect of stochastic control. It presents the results in the context of finite and infinite horizon problems, and discusses a number of new and interesting issues. Further, it precisely identifies, for the first time, the interconnections between three well-known, relevant issues – the existence of optimal controls, solvability of the optimality system, and solvability of the associated Riccati equation. Although the content is largely self-contained, readers should have a basic grasp of linear algebra, functional analysis and stochastic ordinary differential equations. The book is mainly intended for senior undergraduate and graduate students majoring in applied mathematics who are interested in stochastic control theory. However, it will also appeal to researchers in other related areas, such as engineering, management, finance/economics and the social sciences.
Constrained Optimization Of Linear Systems For Infinite Horizon Problems
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Author : Charles Roger Glassey
language : en
Publisher:
Release Date : 1965
Constrained Optimization Of Linear Systems For Infinite Horizon Problems written by Charles Roger Glassey and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Control theory categories.
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).
Nonlinear Model Predictive Control
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Author : Lars Grüne
language : en
Publisher: Springer
Release Date : 2018-06-28
Nonlinear Model Predictive Control written by Lars Grüne and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-28 with Technology & Engineering categories.
This book offers readers a thorough and rigorous introduction to nonlinear model predictive control (NMPC) for discrete-time and sampled-data systems. NMPC schemes with and without stabilizing terminal constraints are detailed, and intuitive examples illustrate the performance of different NMPC variants. NMPC is interpreted as an approximation of infinite-horizon optimal control so that important properties like closed-loop stability, inverse optimality and suboptimality can be derived in a uniform manner. These results are complemented by discussions of feasibility and robustness. An introduction to nonlinear optimal control algorithms yields essential insights into how the nonlinear optimization routine—the core of any nonlinear model predictive controller—works. Accompanying software in MATLAB® and C++ (downloadable from extras.springer.com/), together with an explanatory appendix in the book itself, enables readers to perform computer experiments exploring the possibilities and limitations of NMPC. The second edition has been substantially rewritten, edited and updated to reflect the significant advances that have been made since the publication of its predecessor, including: • a new chapter on economic NMPC relaxing the assumption that the running cost penalizes the distance to a pre-defined equilibrium; • a new chapter on distributed NMPC discussing methods which facilitate the control of large-scale systems by splitting up the optimization into smaller subproblems; • an extended discussion of stability and performance using approximate updates rather than full optimization; • replacement of the pivotal sufficient condition for stability without stabilizing terminal conditions with a weaker alternative and inclusion of an alternative and much simpler proof in the analysis; and • further variations and extensions in response to suggestions from readers of the first edition. Though primarily aimed at academic researchers and practitioners working in control and optimization, the text is self-contained, featuring background material on infinite-horizon optimal control and Lyapunov stability theory that also makes it accessible for graduate students in control engineering and applied mathematics.
H Infinity Optimal Control And Related
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Author : Basar
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
H Infinity Optimal Control And Related written by Basar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Science categories.
One of the major concentrated activities of the past decade in control theory has been the development of the so-called "HOO-optimal control theory," which addresses the issue of worst-case controller design for linear plants subject to unknown additive disturbances, including problems of disturbance attenuation, model matching, and tracking. The mathematical OO symbol "H " stands for the Hardy space of all complex-valued functions of a complex variable, which are analytic and bounded in the open right half complex plane. For a linear (continuous-time, time-invariant) plant, oo the H norm of the transfer matrix is the maximum of its largest singular value over all frequencies. OO Controller design problems where the H norm plays an important role were initially formulated by George Zames in the early 1980's, in the context of sensitivity reduction in linear plants, with the design problem posed as a mathematical optimization problem using an (HOO) operator norm. Thus formulated originally in the frequency domain, the main tools used during the early phases of research on this class of problems have been operator and approximation theory, spectral factorization, and (Youla) parametrization, leading initially to rather complicated (high-dimensional) OO optimal or near-optimal (under the H norm) controllers.
Optimal Control Problems Arising In Forest Management
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Author : Alexander J. Zaslavski
language : en
Publisher: Springer
Release Date : 2019-08-16
Optimal Control Problems Arising In Forest Management written by Alexander J. Zaslavski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-16 with Mathematics categories.
This book is devoted to the study of optimal control problems arising in forest management, an important and fascinating topic in mathematical economics studied by many researchers over the years. The volume studies the forest management problem by analyzing a class of optimal control problems that contains it and showing the existence of optimal solutions over infinite horizon. It also studies the structure of approximate solutions on finite intervals and their turnpike properties, as well as the stability of the turnpike phenomenon and the structure of approximate solutions on finite intervals in the regions close to the end points. The book is intended for mathematicians interested in the optimization theory, optimal control and their applications to the economic theory.