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Optimal Control and Geometry: Integrable Systems
by Velimir JurdjevicThe synthesis of symplectic geometry, the calculus of variations and control theory offered in this book provides a crucial foundation for the understanding of many problems in applied mathematics. Focusing on the theory of integrable systems, this book introduces a class of optimal control problems on Lie groups, whose Hamiltonians, obtained through the Maximum Principle of optimality, shed new light on the theory of integrable systems. These Hamiltonians provide an original and unified account of the existing theory of integrable systems. The book particularly explains much of the mystery surrounding the Kepler problem, the Jacobi problem and the Kovalevskaya Top. It also reveals the ubiquitous presence of elastic curves in integrable systems up to the soliton solutions of the non-linear Schroedinger's equation. Containing a useful blend of theory and applications, this is an indispensable guide for graduates and researchers in many fields, from mathematical physics to space control.
Optimal Control and Optimization of Stochastic Supply Chain Systems
by Dong-Ping SongOptimal Control and Optimization of Stochastic Supply Chain Systems examines its subject the context of the presence of a variety of uncertainties. Numerous examples with intuitive illustrations and tables are provided, to demonstrate the structural characteristics of the optimal control policies in various stochastic supply chains and to show how to make use of these characteristics to construct easy-to-operate sub-optimal policies. In Part I, a general introduction to stochastic supply chain systems is provided. Analytical models for various stochastic supply chain systems are formulated and analysed in Part II. In Part III the structural knowledge of the optimal control policies obtained in Part II is utilized to construct easy-to-operate sub-optimal control policies for various stochastic supply chain systems accordingly. Finally, Part IV discusses the optimisation of threshold-type control policies and their robustness. A key feature of the book is its tying together of the complex analytical models produced by the requirements of operational practice, and the simple solutions needed for implementation. The analytical models and theoretical analysis propounded in this monograph will be of benefit to academic researchers and graduate students looking at logistics and supply chain management from standpoints in operations research or industrial, manufacturing, or control engineering. The practical tools and solutions and the qualitative insights into the ideas underlying functional supply chain systems will be of similar use to readers from more industrially-based backgrounds.
Optimal Control Applied to Biological Models (Chapman & Hall/CRC Mathematical Biology Series)
by Suzanne Lenhart John T. WorkmanFrom economics and business to the biological sciences to physics and engineering, professionals successfully use the powerful mathematical tool of optimal control to make management and strategy decisions. Optimal Control Applied to Biological Models thoroughly develops the mathematical aspects of optimal control theory and provides insight into t
Optimal Control of Differential Equations
by Nicolae H. Pavel"Based on the International Conference on Optimal Control of Differential Equations held recently at Ohio University, Athens, this Festschrift to honor the sixty-fifth birthday of Constantin Corduneanu an outstanding researcher in differential and integral equations provides in-depth coverage of recent advances, applications, and open problems relevant to mathematics and physics. Introduces new results as well as novel methods and techniques!"
Optimal Control of PDEs under Uncertainty: An Introduction with Application to Optimal Shape Design of Structures (SpringerBriefs in Mathematics)
by Jesús Martínez-Frutos Francisco Periago EsparzaThis book provides a direct and comprehensive introduction to theoretical and numerical concepts in the emerging field of optimal control of partial differential equations (PDEs) under uncertainty. The main objective of the book is to offer graduate students and researchers a smooth transition from optimal control of deterministic PDEs to optimal control of random PDEs. Coverage includes uncertainty modelling in control problems, variational formulation of PDEs with random inputs, robust and risk-averse formulations of optimal control problems, existence theory and numerical resolution methods. The exposition focusses on the entire path, starting from uncertainty modelling and ending in the practical implementation of numerical schemes for the numerical approximation of the considered problems. To this end, a selected number of illustrative examples are analysed in detail throughout the book. Computer codes, written in MatLab, are provided for all these examples. This book is adressed to graduate students and researches in Engineering, Physics and Mathematics who are interested in optimal control and optimal design for random partial differential equations.
Optimal Control of Stochastic Difference Volterra Equations
by Leonid ShaikhetThis book showcases a subclass of hereditary systems, that is, systems with behaviour depending not only on their current state but also on their past history; it is an introduction to the mathematical theory of optimal control for stochastic difference Volterra equations of neutral type. As such, it will be of much interest to researchers interested in modelling processes in physics, mechanics, automatic regulation, economics and finance, biology, sociology and medicine for all of which such equations are very popular tools. The text deals with problems of optimal control such as meeting given performance criteria, and stabilization, extending them to neutral stochastic difference Volterra equations. In particular, it contrasts the difference analogues of solutions to optimal control and optimal estimation problems for stochastic integral Volterra equations with optimal solutions for corresponding problems in stochastic difference Volterra equations. Optimal Control of Stochastic Difference Volterra Equations commences with an historical introduction to the emergence of this type of equation with some additional mathematical preliminaries. It then deals with the necessary conditions for optimality in the control of the equations and constructs a feedback control scheme. The approximation of stochastic quasilinear Volterra equations with quadratic performance functionals is then considered. Optimal stabilization is discussed and the filtering problem formulated. Finally, two methods of solving the optimal control problem for partly observable linear stochastic processes, also with quadratic performance functionals, are developed. Integrating the author's own research within the context of the current state-of-the-art of research in difference equations, hereditary systems theory and optimal control, this book is addressed to specialists in mathematical optimal control theory and to graduate students in pure and applied mathematics and control engineering.
Optimal Control of the Growth of Wealth of Nations (Stability and Control: Theory, Methods and Applications)
by E.N. ChukwuStudents and researchers in applied mathematics and applied economics can use this introductory-level graduate text. It looks at the current problems of the development of the global economy by studying the dynamics of key economic variables, such as gross national product, interest rates, employment, value of capital stock, prices (inflation) and
Optimal Control Problems Arising in Forest Management (SpringerBriefs in Optimization)
by Alexander J. ZaslavskiThis 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.
Optimal Control Problems Related to the Robinson–Solow–Srinivasan Model (Monographs in Mathematical Economics #4)
by Alexander J. ZaslavskiThis book is devoted to the study of classes of optimal control problems arising in economic growth theory, related to the Robinson–Solow–Srinivasan (RSS) model. The model was introduced in the 1960s by economists Joan Robinson, Robert Solow, and Thirukodikaval Nilakanta Srinivasan and was further studied by Robinson, Nobuo Okishio, and Joseph Stiglitz. Since then, the study of the RSS model has become an important element of economic dynamics. In this book, two large general classes of optimal control problems, both of them containing the RSS model as a particular case, are presented for study. For these two classes, a turnpike theory is developed and the existence of solutions to the corresponding infinite horizon optimal control problems is established. The book contains 9 chapters. Chapter 1 discusses turnpike properties for some optimal control problems that are known in the literature, including problems corresponding to the RSS model. The first class of optimal control problems is studied in Chaps. 2–6. In Chap. 2, infinite horizon optimal control problems with nonautonomous optimality criteria are considered. The utility functions, which determine the optimality criterion, are nonconcave. This class of models contains the RSS model as a particular case. The stability of the turnpike phenomenon of the one-dimensional nonautonomous concave RSS model is analyzed in Chap. 3. The following chapter takes up the study of a class of autonomous nonconcave optimal control problems, a subclass of problems considered in Chap. 2. The equivalence of the turnpike property and the asymptotic turnpike property, as well as the stability of the turnpike phenomenon, is established. Turnpike conditions and the stability of the turnpike phenomenon for nonautonomous problems are examined in Chap. 5, with Chap. 6 devoted to the study of the turnpike properties for the one-dimensional nonautonomous nonconcave RSS model. The utility functions, which determine the optimality criterion, are nonconcave. The class of RSS models is identified with a complete metric space of utility functions. Using the Baire category approach, the turnpike phenomenon is shown to hold for most of the models. Chapter 7 begins the study of the second large class of autonomous optimal control problems, and turnpike conditions are established. The stability of the turnpike phenomenon for this class of problems is investigated further in Chaps. 8 and 9.
Optimal Control Theory: Applications to Management Science and Economics (Springer Texts in Business and Economics)
by Suresh P. SethiThis new 4th edition offers an introduction to optimal control theory and its diverse applications in management science and economics. It introduces students to the concept of the maximum principle in continuous (as well as discrete) time by combining dynamic programming and Kuhn-Tucker theory. While some mathematical background is needed, the emphasis of the book is not on mathematical rigor, but on modeling realistic situations encountered in business and economics. It applies optimal control theory to the functional areas of management including finance, production and marketing, as well as the economics of growth and of natural resources. In addition, it features material on stochastic Nash and Stackelberg differential games and an adverse selection model in the principal-agent framework. Exercises are included in each chapter, while the answers to selected exercises help deepen readers’ understanding of the material covered. Also included are appendices of supplementary material on the solution of differential equations, the calculus of variations and its ties to the maximum principle, and special topics including the Kalman filter, certainty equivalence, singular control, a global saddle point theorem, Sethi-Skiba points, and distributed parameter systems. Optimal control methods are used to determine optimal ways to control a dynamic system. The theoretical work in this field serves as the foundation for the book, in which the author applies it to business management problems developed from his own research and classroom instruction. The new edition has been refined and updated, making it a valuable resource for graduate courses on applied optimal control theory, but also for financial and industrial engineers, economists, and operational researchers interested in applying dynamic optimization in their fields.
Optimal Control Theory and Static Optimization in Economics
by Daniel Leonard Ngo Van LongOptimal control theory is a technique being used increasingly by academic economists to study problems involving optimal decisions in a multi-period framework. This book is designed to make the difficult subject of optimal control theory easily accessible to economists while at the same time maintaining rigor. Economic intuition is emphasized, examples and problem sets covering a wide range of applications in economics are provided, theorems are clearly stated and their proofs are carefully explained. The development of the text is gradual and fully integrated, beginning with the simple formulations and progressing to advanced topics. Optimal control theory is introduced directly, without recourse to the calculus of variations, and the connection with the latter and with dynamic programming is explained in a separate chapter. Also, the book draws the parallel between optimal control theory and static optimization. No previous knowledge of differential equations is required.
Optimal Covariate Designs
by Premadhis Das Ganesh Dutta Nripes Kumar Mandal Bikas Kumar SinhaThis book primarily addresses the optimality aspects of covariate designs. A covariate model is a combination of ANOVA and regression models. Optimal estimation of the parameters of the model using a suitable choice of designs is of great importance; as such choices allow experimenters to extract maximum information for the unknown model parameters. The main emphasis of this monograph is to start with an assumed covariate model in combination with some standard ANOVA set-ups such as CRD, RBD, BIBD, GDD, BTIBD, BPEBD, cross-over, multi-factor, split-plot and strip-plot designs, treatment control designs, etc. and discuss the nature and availability of optimal covariate designs. In some situations, optimal estimations of both ANOVA and the regression parameters are provided. Global optimality and D-optimality criteria are mainly used in selecting the design. The standard optimality results of both discrete and continuous set-ups have been adapted, and several novel combinatorial techniques have been applied for the construction of optimum designs using Hadamard matrices, the Kronecker product, Rao-Khatri product, mixed orthogonal arrays to name a few.
Optimal Coverage in Wireless Sensor Networks (Springer Optimization and Its Applications #162)
by Weili Wu Zhao Zhang Wonjun Lee Ding-Zhu DuThis book will serve as a reference, presenting state-of-the-art research on theoretical aspects of optimal sensor coverage problems. Readers will find it a useful tool for furthering developments on theory and applications of optimal coverage; much of the content can serve as material for advanced topics courses at the graduate level. The book is well versed with the hottest research topics such as Lifetime of Coverage, Weighted Sensor Cover, k-Coverage, Heterogeneous Sensors, Barrier, Sweep and Partial Coverage, Mobile Sensors, Camera Sensors and Energy-Harvesting Sensors, and more. Topics are introduced in a natural order from simple covers to connected covers, to the lifetime problem. Later, the book begins revisiting earlier problems ranging from the introduction of weights to coverage by k sensors and partial coverage, and from sensor heterogeneity to novel problems such as the barrier coverage problem. The book ends with coverage of mobile sensors, camera sensors, energy-harvesting sensors, underwater sensors, and crowdsensing.
Optimal Design for Nonlinear Response Models
by Valerii V. Fedorov Sergei L. LeonovOptimal Design for Nonlinear Response Models discusses the theory and applications of model-based experimental design with a strong emphasis on biopharmaceutical studies. The book draws on the authors' many years of experience in academia and the pharmaceutical industry. While the focus is on nonlinear models, the book begins with an explanation of
Optimal Design of Control Systems: Stochastic and Deterministic Problems (Pure and Applied Mathematics: A Series of Monographs and Textbooks/221)
by Gennadii E. Kolosov"Covers design methods for optimal (or quasioptimal) control algorithms in the form of synthesis for deterministic and stochastic dynamical systems-with applications in aerospace, robotic, and servomechanical technologies. Providing new results on exact and approximate solutions of optimal control problems."
Optimal Design of Queueing Systems
by Shaler Stidham Jr.The First Comprehensive Book on the SubjectFocusing on the underlying structure of a system, Optimal Design of Queueing Systems explores how to set the parameters of a queueing system, such as arrival and service rates, before putting it into operation. It considers various objectives, comparing individually optimal (Nash equilibrium), socially opt
Optimal Design through the Sub-Relaxation Method
by Pablo PedregalThis book provides a comprehensive guide to analyzing and solving optimal design problems in continuous media by means of the so-called sub-relaxation method. Though the underlying ideas are borrowed from other, more classical approaches, here they are used and organized in a novel way, yielding a distinct perspective on how to approach this kind of optimization problems. Starting with a discussion of the background motivation, the book broadly explains the sub-relaxation method in general terms, helping readers to grasp, from the very beginning, the driving idea and where the text is heading. In addition to the analytical content of the method, it examines practical issues like optimality and numerical approximation. Though the primary focus is on the development of the method for the conductivity context, the book's final two chapters explore several extensions of the method to other problems, as well as formal proofs. The text can be used for a graduate course in optimal design, even if the method would require some familiarity with the main analytical issues associated with this type of problems. This can be addressed with the help of the provided bibliography.
Optimal Districting and Territory Design (International Series in Operations Research & Management Science #284)
by Roger Z. Ríos-MercadoThis book highlights recent advances in the field of districting, territory design, and zone design. Districting problems deal essentially with tactical decisions, and involve mainly dividing a set of geographic units into clusters or territories subject to some planning requirements. This book presents models, theory, algorithms (exact or heuristic), and applications that would bring research on districting systems up-to-date and define the state-of-the-art. Although papers have addressed real-world problems that require districting or territory division decisions, this is the first comprehensive book that directly addresses these problems. The chapters capture the diverse nature of districting applications, as the book is divided into three different areas of research. Part I covers recent up-to-date surveys on important areas of districting such as police districting, health care districting, and districting algorithms based on computational geometry. Part II focuses on recent advances on theory, modeling, and algorithms including mathematical programming and heuristic approaches, and finally, Part III contains successful applications in real-world districting cases.
Optimal Estimation of Dynamic Systems (Chapman & Hall/CRC Applied Mathematics & Nonlinear Science)
by John L. Crassidis John L. JunkinsAn ideal self-study guide for practicing engineers as well as senior undergraduate and beginning graduate students, this book highlights the importance of both physical and numerical modeling in solving dynamics-based estimation problems found in engineering systems, such as spacecraft attitude determination, GPS navigation, orbit determination, and aircraft tracking. With more than 100 pages of new material, this reorganized and expanded edition incorporates new theoretical results, a new chapter on advanced sequential state estimation, and additional examples and exercises. MATLAB codes are available on the book's website.
Optimal Experimental Design: A Concise Introduction for Researchers (Lecture Notes in Statistics #226)
by Jesús López-FidalgoThis textbook provides a concise introduction to optimal experimental design and efficiently prepares the reader for research in the area. It presents the common concepts and techniques for linear and nonlinear models as well as Bayesian optimal designs. The last two chapters are devoted to particular themes of interest, including recent developments and hot topics in optimal experimental design, and real-world applications. Numerous examples and exercises are included, some of them with solutions or hints, as well as references to the existing software for computing designs. The book is primarily intended for graduate students and young researchers in statistics and applied mathematics who are new to the field of optimal experimental design. Given the applications and the way concepts and results are introduced, parts of the text will also appeal to engineers and other applied researchers.
Optimal Experimental Design for Non-Linear Models
by Christos P. KitsosThis book tackles the Optimal Non-Linear Experimental Design problem from an applications perspective. At the same time it offers extensive mathematical background material that avoids technicalities, making it accessible to non-mathematicians: Biologists, Medical Statisticians, Sociologists, Engineers, Chemists and Physicists will find new approaches to conducting their experiments. The book is recommended for Graduate Students and Researchers.
Optimal Experimental Design with R
by Dieter Rasch Jurgen Pilz L.R. Verdooren Albrecht GebhardtExperimental design is often overlooked in the literature of applied and mathematical statistics: statistics is taught and understood as merely a collection of methods for analyzing data. Consequently, experimenters seldom think about optimal design, including prerequisites such as the necessary sample size needed for a precise answer for an experi
Optimal Fractional-order Predictive PI Controllers: For Process Control Applications with Additional Filtering (Studies in Infrastructure and Control)
by Arun Mozhi Panneer Selvam Fawnizu Azmadi Hussin Rosdiazli Ibrahim Kishore Bingi Nagarajapandian M.This book presents the study to design, develop, and implement improved PI control techniques using dead-time compensation, structure enhancements, learning functions and fractional ordering parameters. Two fractional-order PI controllers are proposed and designed: fractional-order predictive PI and hybrid iterative learning based fractional-order predictive PI controller. Furthermore, the proposed fractional-order control strategies and filters are simulated over first- and second-order benchmark process models and further validated using the real-time experimentation of the pilot pressure process plant. In this book, five chapters are structured with a proper sequential flow of details to provide a better understanding for the readers. A general introduction to the controllers, filters and optimization techniques is presented in Chapter 1. Reviews of the PI controllers family and their modifications are shown in the initial part of Chapter 2, followed by the development of the proposed fractional-order predictive PI (FOPPI) controller with dead-time compensation ability. In the first part of chapter 3, a review of the PI based iterative learning controllers, modified structures of the ILC and their modifications are presented. Then, the design of the proposed hybrid iterative learning controller-based fractional-order predictive PI controller based on the current cyclic feedback structure is presented. Lastly, the results and discussion of the proposed controller on benchmark process models and the real-time experimentation of the pilot pressure process plant are given. Chapter 4 presents the development of the proposed filtering techniques and their performance comparison with the conventional methods. Chapter 5 proposes the improvement of the existing sine cosine algorithm (SCA) and arithmetic optimization algorithm (AOA) to form a novel arithmetic-trigonometric optimization algorithm (ATOA) to accelerate the rate of convergence in lesser iterations with mitigation towards getting caught in the same local position. The performance analysis of the optimization algorithm will be carried out on benchmark test functions and the real-time pressure process plant.
The Optimal Homotopy Asymptotic Method
by Vasile Marinca Nicolae HerisanuThis book emphasizes in detail the applicability of the Optimal Homotopy Asymptotic Method to various engineering problems. It is a continuation of the book "Nonlinear Dynamical Systems in Engineering: Some Approximate Approaches", published at Springer in 2011 and it contains a great amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines and so on. The main structure of the book consists of 5 chapters. The first chapter is introductory while the second chapter is devoted to a short history of the development of homotopy methods, including the basic ideas of the Optimal Homotopy Asymptotic Method. The last three chapters, from Chapter 3 to Chapter 5, are introducing three distinct alternatives of the Optimal Homotopy Asymptotic Method with illustrative applications to nonlinear dynamical systems. The third chapter deals with the first alternative of our approach with two iterations. Five applications are presented from fluid mechanics and nonlinear oscillations. The Chapter 4 presents the Optimal Homotopy Asymptotic Method with a single iteration and solving the linear equation on the first approximation. Here are treated 32 models from different fields of engineering such as fluid mechanics, thermodynamics, nonlinear damped and undamped oscillations, electrical machines and even from physics and biology. The last chapter is devoted to the Optimal Homotopy Asymptotic Method with a single iteration but without solving the equation in the first approximation.
Optimal Impulsive Control: The Extension Approach (Lecture Notes in Control and Information Sciences #477)
by Fernando Lobo Pereira Dmitry Karamzin Aram ArutyunovOptimal Impulsive Control explores the class of impulsive dynamic optimization problems—problems that stem from the fact that many conventional optimal control problems do not have a solution in the classical setting—which is highly relevant with regard to engineering applications. The absence of a classical solution naturally invokes the so-called extension, or relaxation, of a problem, and leads to the notion of generalized solution which encompasses the notions of generalized control and trajectory; in this book several extensions of optimal control problems are considered within the framework of optimal impulsive control theory. In this framework, the feasible arcs are permitted to have jumps, while the conventional absolutely continuous trajectories may fail to exist. The authors draw together various types of their own results, centered on the necessary conditions of optimality in the form of Pontryagin’s maximum principle and the existence theorems, which shape a substantial body of optimal impulsive control theory. At the same time, they present optimal impulsive control theory in a unified framework, introducing the different paradigmatic problems in increasing order of complexity. The rationale underlying the book involves addressing extensions increasing in complexity from the simplest case provided by linear control systems and ending with the most general case of a totally nonlinear differential control system with state constraints.The mathematical models presented in Optimal Impulsive Control being encountered in various engineering applications, this book will be of interest to both academic researchers and practising engineers.