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Robust Engineering Designs of Partial Differential Systems and Their Applications

Author: Bor-Sen Chen

Publisher: CRC Press

Published: 2021-12-23

Total Pages: 255

ISBN-13: 1000514099

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Most systems in science, engineering, and biology are of partial differential systems (PDSs) modeled by partial differential equations. Many books about partial differential equations have been written by mathematicians and mainly address some fundamental mathematic backgrounds and discuss some mathematic properties of partial differential equations. Only a few books on PDSs have been written by engineers; however, these books have focused mainly on the theoretical stabilization analysis of PDSs, especially mechanical systems. This book investigates both robust stabilization control design and robust filter design and reference tracking control design in mechanical, signal processing, and control systems to fill a gap in the study of PDSs. Robust Engineering Designs of Partial Differential Systems and Their Applications offers some fundamental background in the first two chapters. The rest of the chapters focus on a specific design topic with a corresponding deep investigation into robust H∞ filtering, stabilization, or tracking design for more complex and practical PDSs under stochastic fluctuation and external disturbance. This book is aimed at engineers and scientists and addresses the gap between the theoretical stabilization results of PDSs in academic and practical engineering designs more focused on the robust H∞ filtering, stabilization, and tracking control problems of linear and nonlinear PDSs under intrinsic random fluctuation and external disturbance in industrial applications. Part I provides backgrounds on PDSs, such as Galerkin’s, and finite difference methods to approximate PDSs and a fuzzy method to approximate nonlinear PDSs. Part II examines robust H∞ filter designs for the robust state estimation of linear and nonlinear stochastic PDSs. And Part III treats robust H∞ stabilization and tracking control designs of linear and nonlinear PDSs. Every chapter focuses on an engineering design topic with both theoretical design analysis and practical design examples.

Book Synopsis Robust Engineering Designs of Partial Differential Systems and Their Applications by : Bor-Sen Chen

Download or read book Robust Engineering Designs of Partial Differential Systems and Their Applications written by Bor-Sen Chen and published by CRC Press. This book was released on 2021-12-23 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most systems in science, engineering, and biology are of partial differential systems (PDSs) modeled by partial differential equations. Many books about partial differential equations have been written by mathematicians and mainly address some fundamental mathematic backgrounds and discuss some mathematic properties of partial differential equations. Only a few books on PDSs have been written by engineers; however, these books have focused mainly on the theoretical stabilization analysis of PDSs, especially mechanical systems. This book investigates both robust stabilization control design and robust filter design and reference tracking control design in mechanical, signal processing, and control systems to fill a gap in the study of PDSs. Robust Engineering Designs of Partial Differential Systems and Their Applications offers some fundamental background in the first two chapters. The rest of the chapters focus on a specific design topic with a corresponding deep investigation into robust H∞ filtering, stabilization, or tracking design for more complex and practical PDSs under stochastic fluctuation and external disturbance. This book is aimed at engineers and scientists and addresses the gap between the theoretical stabilization results of PDSs in academic and practical engineering designs more focused on the robust H∞ filtering, stabilization, and tracking control problems of linear and nonlinear PDSs under intrinsic random fluctuation and external disturbance in industrial applications. Part I provides backgrounds on PDSs, such as Galerkin’s, and finite difference methods to approximate PDSs and a fuzzy method to approximate nonlinear PDSs. Part II examines robust H∞ filter designs for the robust state estimation of linear and nonlinear stochastic PDSs. And Part III treats robust H∞ stabilization and tracking control designs of linear and nonlinear PDSs. Every chapter focuses on an engineering design topic with both theoretical design analysis and practical design examples.

Robust Engineering Designs of Partial Differential Systems and Their Applications

Author: Bor-Sen Chen

Publisher: CRC Press

Published: 2021-12-22

Total Pages: 459

ISBN-13: 1000514064

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Considers both time‐domain and frequency domain robust design techniques of partial differential systems Illustrates both theoretical robust design techniques and practical applications Discusses partial differential systems with both Dirichlet and Neuman boundary conditions in robust design procedure Addresses deterministic and stochastic partial differential systems Explores theoretical mathematical background, robust signal processing design, robust control system design and robust biological system design with application

Book Synopsis Robust Engineering Designs of Partial Differential Systems and Their Applications by : Bor-Sen Chen

Optimal Control of PDEs under Uncertainty

Author: Jesús Martínez-Frutos

Publisher: Springer

Published: 2018-08-30

Total Pages: 123

ISBN-13: 3319982109

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This 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.

Book Synopsis Optimal Control of PDEs under Uncertainty by : Jesús Martínez-Frutos

Download or read book Optimal Control of PDEs under Uncertainty written by Jesús Martínez-Frutos and published by Springer. This book was released on 2018-08-30 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 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.

Nonlinear and Robust Control of PDE Systems

Author: Panagiotis D. Christofides

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 262

ISBN-13: 1461201853

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The interest in control of nonlinear partial differential equation (PDE) sys tems has been triggered by the need to achieve tight distributed control of transport-reaction processes that exhibit highly nonlinear behavior and strong spatial variations. Drawing from recent advances in dynamics of PDE systems and nonlinear control theory, control of nonlinear PDEs has evolved into a very active research area of systems and control. This book the first of its kind- presents general methods for the synthesis of nonlinear and robust feedback controllers for broad classes of nonlinear PDE sys tems and illustrates their applications to transport-reaction processes of industrial interest. Specifically, our attention focuses on quasi-linear hyperbolic and parabolic PDE systems for which the manipulated inputs and measured and controlled outputs are distributed in space and bounded. We use geometric and Lyapunov-based control techniques to synthesize nonlinear and robust controllers that use a finite number of measurement sensors and control actuators to achieve stabilization of the closed-loop system, output track ing, and attenuation of the effect of model uncertainty. The controllers are successfully applied to numerous convection-reaction and diffusion-reaction processes, including a rapid thermal chemical vapor deposition reactor and a Czochralski crystal growth process. The book includes comparisons of the proposed nonlinear and robust control methods with other approaches and discussions of practical implementation issues.

Book Synopsis Nonlinear and Robust Control of PDE Systems by : Panagiotis D. Christofides

Download or read book Nonlinear and Robust Control of PDE Systems written by Panagiotis D. Christofides and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interest in control of nonlinear partial differential equation (PDE) sys tems has been triggered by the need to achieve tight distributed control of transport-reaction processes that exhibit highly nonlinear behavior and strong spatial variations. Drawing from recent advances in dynamics of PDE systems and nonlinear control theory, control of nonlinear PDEs has evolved into a very active research area of systems and control. This book the first of its kind- presents general methods for the synthesis of nonlinear and robust feedback controllers for broad classes of nonlinear PDE sys tems and illustrates their applications to transport-reaction processes of industrial interest. Specifically, our attention focuses on quasi-linear hyperbolic and parabolic PDE systems for which the manipulated inputs and measured and controlled outputs are distributed in space and bounded. We use geometric and Lyapunov-based control techniques to synthesize nonlinear and robust controllers that use a finite number of measurement sensors and control actuators to achieve stabilization of the closed-loop system, output track ing, and attenuation of the effect of model uncertainty. The controllers are successfully applied to numerous convection-reaction and diffusion-reaction processes, including a rapid thermal chemical vapor deposition reactor and a Czochralski crystal growth process. The book includes comparisons of the proposed nonlinear and robust control methods with other approaches and discussions of practical implementation issues.

Multi-Objective Optimization System Designs and Their Applications

Author: Bor-Sen Chen

Publisher: CRC Press

Published: 2023-12-05

Total Pages: 292

ISBN-13: 1000999521

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This book introduces multi-objective design methods to solve multi-objective optimization problems (MOPs) of linear/nonlinear dynamic systems under intrinsic random fluctuation and external disturbance. The MOPs of multiple targets for systems are all transformed into equivalent linear matrix inequality (LMI)-constrained MOPs. Corresponding reverse-order LMI-constrained multi-objective evolution algorithms are introduced to solve LMI-constrained MOPs using MATLAB®. All proposed design methods are based on rigorous theoretical results, and their applications are focused on more practical engineering design examples. Features: Discusses multi-objective optimization from an engineer’s perspective. Contains the theoretical design methods of multi-objective optimization schemes. Includes a wide spectrum of recent research topics in control design, especially for stochastic mean field diffusion problems. Covers practical applications in each chapter, like missile guidance design, economic and financial systems, power control tracking, minimization design in communication, and so forth. Explores practical multi-objective optimization design examples in control, signal processing, communication, and cyber-financial systems. This book is aimed at researchers and graduate students in electrical engineering, control design, and optimization.

Book Synopsis Multi-Objective Optimization System Designs and Their Applications by : Bor-Sen Chen

Download or read book Multi-Objective Optimization System Designs and Their Applications written by Bor-Sen Chen and published by CRC Press. This book was released on 2023-12-05 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces multi-objective design methods to solve multi-objective optimization problems (MOPs) of linear/nonlinear dynamic systems under intrinsic random fluctuation and external disturbance. The MOPs of multiple targets for systems are all transformed into equivalent linear matrix inequality (LMI)-constrained MOPs. Corresponding reverse-order LMI-constrained multi-objective evolution algorithms are introduced to solve LMI-constrained MOPs using MATLAB®. All proposed design methods are based on rigorous theoretical results, and their applications are focused on more practical engineering design examples. Features: Discusses multi-objective optimization from an engineer’s perspective. Contains the theoretical design methods of multi-objective optimization schemes. Includes a wide spectrum of recent research topics in control design, especially for stochastic mean field diffusion problems. Covers practical applications in each chapter, like missile guidance design, economic and financial systems, power control tracking, minimization design in communication, and so forth. Explores practical multi-objective optimization design examples in control, signal processing, communication, and cyber-financial systems. This book is aimed at researchers and graduate students in electrical engineering, control design, and optimization.

Deterministic Flexibility Analysis

Author: Chuei-Tin Chang

Publisher: CRC Press

Published: 2017-07-28

Total Pages: 230

ISBN-13: 1498748171

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Traditionally, design and control decisions are made in sequential stages over the life cycle of a chemical plant. In the design phase, the optimal operating conditions and the corresponding material and energy balance data are established mainly on the basis of economic considerations. In the subsequent step, the control systems are configured to maintain the key process conditions at the fixed nominal values. Because it is often desirable to address the operability issues at the earliest possible stage before stipulation of control schemes, the systematic incorporation of flexibility analysis in process synthesis and design has received considerable attention in recent years. This book focuses to a large extent on computation and implementation methods of deterministic performance measures, i.e., the steady-state, volumetric, dynamic and temporal flexibility indices, in various applications. The formal definitions of several available performance indices, their mathematical formulations, and the corresponding algorithms and codes are provided in sufficient detail to facilitate implementation. To show the utility of flexibility analyses, the book presents several practical case studies including membrane modules and heat-exchanger networks, solar-driven membrane distillation desalination systems, and hybrid power generation systems. It also includes MATLAB and GAMS codes.

Book Synopsis Deterministic Flexibility Analysis by : Chuei-Tin Chang

Download or read book Deterministic Flexibility Analysis written by Chuei-Tin Chang and published by CRC Press. This book was released on 2017-07-28 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: Traditionally, design and control decisions are made in sequential stages over the life cycle of a chemical plant. In the design phase, the optimal operating conditions and the corresponding material and energy balance data are established mainly on the basis of economic considerations. In the subsequent step, the control systems are configured to maintain the key process conditions at the fixed nominal values. Because it is often desirable to address the operability issues at the earliest possible stage before stipulation of control schemes, the systematic incorporation of flexibility analysis in process synthesis and design has received considerable attention in recent years. This book focuses to a large extent on computation and implementation methods of deterministic performance measures, i.e., the steady-state, volumetric, dynamic and temporal flexibility indices, in various applications. The formal definitions of several available performance indices, their mathematical formulations, and the corresponding algorithms and codes are provided in sufficient detail to facilitate implementation. To show the utility of flexibility analyses, the book presents several practical case studies including membrane modules and heat-exchanger networks, solar-driven membrane distillation desalination systems, and hybrid power generation systems. It also includes MATLAB and GAMS codes.

Partial Differential Equations

Author: Marcelo Epstein

Publisher: Springer

Published: 2017-04-29

Total Pages: 261

ISBN-13: 3319552120

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This monograph presents a graduate-level treatment of partial differential equations (PDEs) for engineers. The book begins with a review of the geometrical interpretation of systems of ODEs, the appearance of PDEs in engineering is motivated by the general form of balance laws in continuum physics. Four chapters are devoted to a detailed treatment of the single first-order PDE, including shock waves and genuinely non-linear models, with applications to traffic design and gas dynamics. The rest of the book deals with second-order equations. In the treatment of hyperbolic equations, geometric arguments are used whenever possible and the analogy with discrete vibrating systems is emphasized. The diffusion and potential equations afford the opportunity of dealing with questions of uniqueness and continuous dependence on the data, the Fourier integral, generalized functions (distributions), Duhamel's principle, Green's functions and Dirichlet and Neumann problems. The target audience primarily comprises graduate students in engineering, but the book may also be beneficial for lecturers, and research experts both in academia in industry.

Book Synopsis Partial Differential Equations by : Marcelo Epstein

Download or read book Partial Differential Equations written by Marcelo Epstein and published by Springer. This book was released on 2017-04-29 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a graduate-level treatment of partial differential equations (PDEs) for engineers. The book begins with a review of the geometrical interpretation of systems of ODEs, the appearance of PDEs in engineering is motivated by the general form of balance laws in continuum physics. Four chapters are devoted to a detailed treatment of the single first-order PDE, including shock waves and genuinely non-linear models, with applications to traffic design and gas dynamics. The rest of the book deals with second-order equations. In the treatment of hyperbolic equations, geometric arguments are used whenever possible and the analogy with discrete vibrating systems is emphasized. The diffusion and potential equations afford the opportunity of dealing with questions of uniqueness and continuous dependence on the data, the Fourier integral, generalized functions (distributions), Duhamel's principle, Green's functions and Dirichlet and Neumann problems. The target audience primarily comprises graduate students in engineering, but the book may also be beneficial for lecturers, and research experts both in academia in industry.

Control and Dynamic Systems V57: Multidisciplinary Engineering Systems: Design and Optimization Techniques and Their Application

Author: C.T. Leonides

Publisher: Academic Press

Published: 2012-12-02

Total Pages: 508

ISBN-13: 0323163092

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Control and Dynamic Systems: Advances in Theory and Applications, Volume 57: Multidisciplinary Engineering Systems: Design and Optimization Techniques and their Application deals with techniques used in the design and optimization of future engineering systems. Comprised of 11 chapters, this book covers techniques for improving product design quality in multidisciplinary systems. These techniques include decomposition techniques for synthesis process; optimization for aircraft systems; actuator and sensor placement; and robust techniques in system design and control process. Students, research workers, and practising engineers will find this book invaluable.

Book Synopsis Control and Dynamic Systems V57: Multidisciplinary Engineering Systems: Design and Optimization Techniques and Their Application by : C.T. Leonides

Download or read book Control and Dynamic Systems V57: Multidisciplinary Engineering Systems: Design and Optimization Techniques and Their Application written by C.T. Leonides and published by Academic Press. This book was released on 2012-12-02 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: Control and Dynamic Systems: Advances in Theory and Applications, Volume 57: Multidisciplinary Engineering Systems: Design and Optimization Techniques and their Application deals with techniques used in the design and optimization of future engineering systems. Comprised of 11 chapters, this book covers techniques for improving product design quality in multidisciplinary systems. These techniques include decomposition techniques for synthesis process; optimization for aircraft systems; actuator and sensor placement; and robust techniques in system design and control process. Students, research workers, and practising engineers will find this book invaluable.

Finite Difference Methods in Financial Engineering

Author: Daniel J. Duffy

Publisher: John Wiley & Sons

Published: 2013-10-28

Total Pages: 452

ISBN-13: 1118856481

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The world of quantitative finance (QF) is one of the fastest growing areas of research and its practical applications to derivatives pricing problem. Since the discovery of the famous Black-Scholes equation in the 1970's we have seen a surge in the number of models for a wide range of products such as plain and exotic options, interest rate derivatives, real options and many others. Gone are the days when it was possible to price these derivatives analytically. For most problems we must resort to some kind of approximate method. In this book we employ partial differential equations (PDE) to describe a range of one-factor and multi-factor derivatives products such as plain European and American options, multi-asset options, Asian options, interest rate options and real options. PDE techniques allow us to create a framework for modeling complex and interesting derivatives products. Having defined the PDE problem we then approximate it using the Finite Difference Method (FDM). This method has been used for many application areas such as fluid dynamics, heat transfer, semiconductor simulation and astrophysics, to name just a few. In this book we apply the same techniques to pricing real-life derivative products. We use both traditional (or well-known) methods as well as a number of advanced schemes that are making their way into the QF literature: Crank-Nicolson, exponentially fitted and higher-order schemes for one-factor and multi-factor options Early exercise features and approximation using front-fixing, penalty and variational methods Modelling stochastic volatility models using Splitting methods Critique of ADI and Crank-Nicolson schemes; when they work and when they don't work Modelling jumps using Partial Integro Differential Equations (PIDE) Free and moving boundary value problems in QF Included with the book is a CD containing information on how to set up FDM algorithms, how to map these algorithms to C++ as well as several working programs for one-factor and two-factor models. We also provide source code so that you can customize the applications to suit your own needs.

Book Synopsis Finite Difference Methods in Financial Engineering by : Daniel J. Duffy

Download or read book Finite Difference Methods in Financial Engineering written by Daniel J. Duffy and published by John Wiley & Sons. This book was released on 2013-10-28 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: The world of quantitative finance (QF) is one of the fastest growing areas of research and its practical applications to derivatives pricing problem. Since the discovery of the famous Black-Scholes equation in the 1970's we have seen a surge in the number of models for a wide range of products such as plain and exotic options, interest rate derivatives, real options and many others. Gone are the days when it was possible to price these derivatives analytically. For most problems we must resort to some kind of approximate method. In this book we employ partial differential equations (PDE) to describe a range of one-factor and multi-factor derivatives products such as plain European and American options, multi-asset options, Asian options, interest rate options and real options. PDE techniques allow us to create a framework for modeling complex and interesting derivatives products. Having defined the PDE problem we then approximate it using the Finite Difference Method (FDM). This method has been used for many application areas such as fluid dynamics, heat transfer, semiconductor simulation and astrophysics, to name just a few. In this book we apply the same techniques to pricing real-life derivative products. We use both traditional (or well-known) methods as well as a number of advanced schemes that are making their way into the QF literature: Crank-Nicolson, exponentially fitted and higher-order schemes for one-factor and multi-factor options Early exercise features and approximation using front-fixing, penalty and variational methods Modelling stochastic volatility models using Splitting methods Critique of ADI and Crank-Nicolson schemes; when they work and when they don't work Modelling jumps using Partial Integro Differential Equations (PIDE) Free and moving boundary value problems in QF Included with the book is a CD containing information on how to set up FDM algorithms, how to map these algorithms to C++ as well as several working programs for one-factor and two-factor models. We also provide source code so that you can customize the applications to suit your own needs.

Stochastic Game Strategies and their Applications

Author: Bor-Sen Chen

Publisher: CRC Press

Published: 2019-07-31

Total Pages: 333

ISBN-13: 0429780508

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Game theory involves multi-person decision making and differential dynamic game theory has been widely applied to n-person decision making problems, which are stimulated by a vast number of applications. This book addresses the gap to discuss general stochastic n-person noncooperative and cooperative game theory with wide applications to control systems, signal processing systems, communication systems, managements, financial systems, and biological systems. H∞ game strategy, n-person cooperative and noncooperative game strategy are discussed for linear and nonlinear stochastic systems along with some computational algorithms developed to efficiently solve these game strategies.

Book Synopsis Stochastic Game Strategies and their Applications by : Bor-Sen Chen

Download or read book Stochastic Game Strategies and their Applications written by Bor-Sen Chen and published by CRC Press. This book was released on 2019-07-31 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: Game theory involves multi-person decision making and differential dynamic game theory has been widely applied to n-person decision making problems, which are stimulated by a vast number of applications. This book addresses the gap to discuss general stochastic n-person noncooperative and cooperative game theory with wide applications to control systems, signal processing systems, communication systems, managements, financial systems, and biological systems. H∞ game strategy, n-person cooperative and noncooperative game strategy are discussed for linear and nonlinear stochastic systems along with some computational algorithms developed to efficiently solve these game strategies.