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Author: Thomas Meurer
Publisher: Springer Science & Business Media
ISBN: 3642300154
Category : Technology & Engineering
Languages : en
Pages : 373
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Book Description
This monograph presents new model-based design methods for trajectory planning, feedback stabilization, state estimation, and tracking control of distributed-parameter systems governed by partial differential equations (PDEs). Flatness and backstepping techniques and their generalization to PDEs with higher-dimensional spatial domain lie at the core of this treatise. This includes the development of systematic late lumping design procedures and the deduction of semi-numerical approaches using suitable approximation methods. Theoretical developments are combined with both simulation examples and experimental results to bridge the gap between mathematical theory and control engineering practice in the rapidly evolving PDE control area. The text is divided into five parts featuring: - a literature survey of paradigms and control design methods for PDE systems - the first principle mathematical modeling of applications arising in heat and mass transfer, interconnected multi-agent systems, and piezo-actuated smart elastic structures - the generalization of flatness-based trajectory planning and feedforward control to parabolic and biharmonic PDE systems defined on general higher-dimensional domains - an extension of the backstepping approach to the feedback control and observer design for parabolic PDEs with parallelepiped domain and spatially and time varying parameters - the development of design techniques to realize exponentially stabilizing tracking control - the evaluation in simulations and experiments Control of Higher-Dimensional PDEs — Flatness and Backstepping Designs is an advanced research monograph for graduate students in applied mathematics, control theory, and related fields. The book may serve as a reference to recent developments for researchers and control engineers interested in the analysis and control of systems governed by PDEs.
Author: Thomas Meurer
Publisher: Springer Science & Business Media
ISBN: 3642300154
Category : Technology & Engineering
Languages : en
Pages : 373
Get Book Here
Book Description
This monograph presents new model-based design methods for trajectory planning, feedback stabilization, state estimation, and tracking control of distributed-parameter systems governed by partial differential equations (PDEs). Flatness and backstepping techniques and their generalization to PDEs with higher-dimensional spatial domain lie at the core of this treatise. This includes the development of systematic late lumping design procedures and the deduction of semi-numerical approaches using suitable approximation methods. Theoretical developments are combined with both simulation examples and experimental results to bridge the gap between mathematical theory and control engineering practice in the rapidly evolving PDE control area. The text is divided into five parts featuring: - a literature survey of paradigms and control design methods for PDE systems - the first principle mathematical modeling of applications arising in heat and mass transfer, interconnected multi-agent systems, and piezo-actuated smart elastic structures - the generalization of flatness-based trajectory planning and feedforward control to parabolic and biharmonic PDE systems defined on general higher-dimensional domains - an extension of the backstepping approach to the feedback control and observer design for parabolic PDEs with parallelepiped domain and spatially and time varying parameters - the development of design techniques to realize exponentially stabilizing tracking control - the evaluation in simulations and experiments Control of Higher-Dimensional PDEs — Flatness and Backstepping Designs is an advanced research monograph for graduate students in applied mathematics, control theory, and related fields. The book may serve as a reference to recent developments for researchers and control engineers interested in the analysis and control of systems governed by PDEs.
Author: Miroslav Krstic
Publisher: SIAM
ISBN: 0898718600
Category : Mathematics
Languages : en
Pages : 197
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Book Description
The text's broad coverage includes parabolic PDEs; hyperbolic PDEs of first and second order; fluid, thermal, and structural systems; delay systems; PDEs with third and fourth derivatives in space (including variants of linearized Ginzburg-Landau, Schrodinger, Kuramoto-Sivashinsky, KdV, beam, and Navier-Stokes equations); real-valued as well as complex-valued PDEs; stabilization as well as motion planning and trajectory tracking for PDEs; and elements of adaptive control for PDEs and control of nonlinear PDEs.
Author: Irena Lasiecka
Publisher: Cambridge University Press
ISBN: 9780521434089
Category : Mathematics
Languages : en
Pages : 678
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Book Description
Originally published in 2000, this is the first volume of a comprehensive two-volume treatment of quadratic optimal control theory for partial differential equations over a finite or infinite time horizon, and related differential (integral) and algebraic Riccati equations. Both continuous theory and numerical approximation theory are included. The authors use an abstract space, operator theoretic approach, which is based on semigroups methods, and which is unifying across a few basic classes of evolution. The various abstract frameworks are motivated by, and ultimately directed to, partial differential equations with boundary/point control. Volume 1 includes the abstract parabolic theory for the finite and infinite cases and corresponding PDE illustrations as well as various abstract hyperbolic settings in the finite case. It presents numerous fascinating results. These volumes will appeal to graduate students and researchers in pure and applied mathematics and theoretical engineering with an interest in optimal control problems.
Author: Irena Lasiecka
Publisher: Cambridge University Press
ISBN: 9780521584012
Category : Mathematics
Languages : en
Pages : 458
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Book Description
Second of a two-volume treatise on deterministic control systems modeled by multi-dimensional partial differential equations.
Author: Randall J. LeVeque
Publisher: SIAM
ISBN: 9780898717839
Category : Mathematics
Languages : en
Pages : 356
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Book Description
This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.
Author: N El Karoui
Publisher: CRC Press
ISBN: 9780582307339
Category : Mathematics
Languages : en
Pages : 236
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Book Description
This book presents the texts of seminars presented during the years 1995 and 1996 at the Université Paris VI and is the first attempt to present a survey on this subject. Starting from the classical conditions for existence and unicity of a solution in the most simple case-which requires more than basic stochartic calculus-several refinements on the hypotheses are introduced to obtain more general results.
Author: Karl Kunisch
Publisher: Springer Science & Business Media
ISBN: 3764389230
Category : Mathematics
Languages : en
Pages : 344
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Book Description
Contains contributions originating from the 'Conference on Optimal Control of Coupled Systems of Partial Differential Equations', held at the 'Mathematisches Forschungsinstitut Oberwolfach' in March 2008. This work covers a range of topics such as controllability, optimality systems, model-reduction techniques, and fluid-structure interactions.
Author: Kirsten A. Morris
Publisher: Springer Nature
ISBN: 3030349497
Category : Technology & Engineering
Languages : en
Pages : 295
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Book Description
This book addresses controller and estimator design for systems that vary both spatially and in time: systems like fluid flow, acoustic noise and flexible structures. It includes coverage of the selection and placement of actuators and sensors for such distributed-parameter systems. The models for distributed parameter systems are coupled ordinary/partial differential equations. Approximations to the governing equations, often of very high order, are required and this complicates both controller design and optimization of the hardware locations. Control system and estimator performance depends not only on the controller/estimator design but also on the location of the hardware. In helping the reader choose the best location for actuators and sensors, the analysis provided in this book is crucial because neither intuition nor trial-and-error is foolproof, especially where multiple sensors and actuators are required, and moving hardware can be difficult and costly. The mechatronic approach advocated, in which controller design is integrated with actuator location, can lead to better performance without increased cost. Similarly, better estimation can be obtained with carefully placed sensors. The text shows how proper hardware placement varies depending on whether, disturbances are present, whether the response should be reduced to an initial condition or whether controllability and/or observability have to be optimized. This book is aimed at non-specialists interested in learning controller design for distributed-parameter systems and the material presented has been used for student teaching. The relevant basic systems theory is presented and followed by a description of controller synthesis using lumped approximations. Numerical algorithms useful for efficient implementation in real engineering systems and practical computational challenges are also described and discussed.
Author: Peter I. Kogut
Publisher: Springer Science & Business Media
ISBN: 0817681493
Category : Science
Languages : en
Pages : 639
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Book Description
In the development of optimal control, the complexity of the systems to which it is applied has increased significantly, becoming an issue in scientific computing. In order to carry out model-reduction on these systems, the authors of this work have developed a method based on asymptotic analysis. Moving from abstract explanations to examples and applications with a focus on structural network problems, they aim at combining techniques of homogenization and approximation. Optimal Control Problems for Partial Differential Equations on Reticulated Domains is an excellent reference tool for graduate students, researchers, and practitioners in mathematics and areas of engineering involving reticulated domains.
Author: Lorenz T. Biegler
Publisher: SIAM
ISBN: 9780898718935
Category : Differential equations, Partial
Languages : en
Pages : 335
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Book Description
Many engineering and scientific problems in design, control, and parameter estimation can be formulated as optimization problems that are governed by partial differential equations (PDEs). The complexities of the PDEs--and the requirement for rapid solution--pose significant difficulties. A particularly challenging class of PDE-constrained optimization problems is characterized by the need for real-time solution, i.e., in time scales that are sufficiently rapid to support simulation-based decision making. Real-Time PDE-Constrained Optimization, the first book devoted to real-time optimization for systems governed by PDEs, focuses on new formulations, methods, and algorithms needed to facilitate real-time, PDE-constrained optimization. In addition to presenting state-of-the-art algorithms and formulations, the text illustrates these algorithms with a diverse set of applications that includes problems in the areas of aerodynamics, biology, fluid dynamics, medicine, chemical processes, homeland security, and structural dynamics. Audience: readers who have expertise in simulation and are interested in incorporating optimization into their simulations, who have expertise in numerical optimization and are interested in adapting optimization methods to the class of infinite-dimensional simulation problems, or who have worked in "offline" optimization contexts and are interested in moving to "online" optimization.
