Partial Differential Equation Based Control Of Nonlinear Systems With Input Delays
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Partial Differential Equation Based Control Of Nonlinear Systems With Input Delays
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Author : Indrasis Chakraborty
language : en
Publisher:
Release Date : 2019-05-31
Partial Differential Equation Based Control Of Nonlinear Systems With Input Delays written by Indrasis Chakraborty and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-31 with Technology & Engineering categories.
Abstract: Partial differential equation (PDE)-based control methods are developed for a class of uncertain nonlinear systems with bounded external disturbances and known/unknown time-varying input delay. Inspired by predictor-based delay compensators, a linear transformation is used to relate the control input to a spatially and time-varying function. The transformation allows the input to be expressed in a manner that separates the control into a delayed control and non-delayed control and also facilitates the ability to compensate for the time-varying aspect of the delay with less complex gain conditions than previous robust control approaches. Unlike previous predictor-based approaches, which inherently depend on the system dynamics, an auxiliary error function is introduced to facilitate a robust control structure that does not depend on known dynamics. The designed controller features gains to compensate for the delay and delay derivative independently and further robustness is achieved since the controller does not require exact model knowledge. In Chapter 2, a tracking controller is developed for a second order system with a known time-varying input delay. A novel Lyapunov-Krasovskii functional is used in the Lyapunov based stability analysis to prove uniform ultimate boundedness of the error signals. Chapter 3 and Chapter 4 focus on the development of a tracking controller for a generalized uncertain nonlinear systems with bounded external disturbances and unknown time-varying input delay. In Chapter 3, a nonlinear mapping is used to map the non-compact time domain to a compact spatial domain, and then a neural network (NN) is used to estimate the unknown time-varying input delay. In Chapter 4, an accelerated gradient descent (AGD) based optimization method is demonstrated to estimate the unknown time-varying delay magnitude. Application of input time-delay for flexible system is examined in Chapter 5. Specifically, an aircraft wing dynamics is considered. The NN based estimation scheme developed in Chapter 3 is combined with a boundary control method, to mitigate oscillations in the aircraft wing in Chapter 5. Dissertation Discovery Company and University of Florida are dedicated to making scholarly works more discoverable and accessible throughout the world. This dissertation, "Partial Differential Equation Based Control of Nonlinear Systems With Input Delays" by Indrasis Chakraborty, was obtained from University of Florida and is being sold with permission from the author. A digital copy of this work may also be found in the university's institutional repository, IR@UF. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation.
Delay Compensation For Nonlinear Adaptive And Pde Systems
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Author : Miroslav Krstic
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-01-23
Delay Compensation For Nonlinear Adaptive And Pde Systems written by Miroslav Krstic 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 2010-01-23 with Mathematics categories.
Shedding light on new opportunities in predictor feedback, this book significantly broadens the set of techniques available to a mathematician or engineer working on delay systems. It is a collection of tools and techniques that make predictor feedback ideas applicable to nonlinear systems, systems modeled by PDEs, systems with highly uncertain or completely unknown input/output delays, and systems whose actuator or sensor dynamics are modeled by more general hyperbolic or parabolic PDEs, rather than by pure delay. Replete with examples, Delay Compensation for Nonlinear, Adaptive, and PDE Systems is an excellent reference guide for graduate students, researchers, and professionals in mathematics, systems control, as well as chemical, mechanical, electrical, computer, aerospace, and civil/structural engineering. Parts of the book may be used in graduate courses on general distributed parameter systems, linear delay systems, PDEs, nonlinear control, state estimator and observers, adaptive control, robust control, or linear time-varying systems.
Nonlinear Control Under Nonconstant Delays
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Author : Nikolaos Bekiaris-Liberis
language : en
Publisher: SIAM
Release Date : 2013-09-25
Nonlinear Control Under Nonconstant Delays written by Nikolaos Bekiaris-Liberis and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-25 with Mathematics categories.
The authors have developed a methodology for control of nonlinear systems in the presence of long delays, with large and rapid variation in the actuation or sensing path, or in the presence of long delays affecting the internal state of a system. In addition to control synthesis, they introduce tools to quantify the performance and the robustness properties of the designs provided in the book. The book is based on the concept of predictor feedback and infinite-dimensional backstepping transformation for linear systems and the authors guide the reader from the basic ideas of the concept?with constant delays only on the input?all the way through to nonlinear systems with state-dependent delays on the input as well as on system states. Readers will find the book useful because the authors provide elegant and systematic treatments of long-standing problems in delay systems, such as systems with state-dependent delays that arise in many applications. In addition, the authors give all control designs by explicit formulae, making the book especially useful for engineers who have faced delay-related challenges and are concerned with actual implementations and they accompany all control designs with Lyapunov-based analysis for establishing stability and performance guarantees.
Nonlinear And Robust Control Of Pde Systems
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Author : Panagiotis D. Christofides
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear And Robust Control Of Pde Systems written by Panagiotis D. Christofides 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 2012-12-06 with Science categories.
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.
Adaptive Control Of Hyperbolic Pdes
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Author : Henrik Anfinsen
language : en
Publisher: Springer
Release Date : 2019-02-21
Adaptive Control Of Hyperbolic Pdes written by Henrik Anfinsen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-21 with Technology & Engineering categories.
Adaptive Control of Linear Hyperbolic PDEs provides a comprehensive treatment of adaptive control of linear hyperbolic systems, using the backstepping method. It develops adaptive control strategies for different combinations of measurements and actuators, as well as for a range of different combinations of parameter uncertainty. The book treats boundary control of systems of hyperbolic partial differential equations (PDEs) with uncertain parameters. The authors develop designs for single equations, as well as any number of coupled equations. The designs are accompanied by mathematical proofs, which allow the reader to gain insight into the technical challenges associated with adaptive control of hyperbolic PDEs, and to get an overview of problems that are still open for further research. Although stabilization of unstable systems by boundary control and boundary sensing are the particular focus, state-feedback designs are also presented. The book also includes simulation examples with implementational details and graphical displays, to give readers an insight into the performance of the proposed control algorithms, as well as the computational details involved. A library of MATLAB® code supplies ready-to-use implementations of the control and estimation algorithms developed in the book, allowing readers to tailor controllers for cases of their particular interest with little effort. These implementations can be used for many different applications, including pipe flows, traffic flow, electrical power lines, and more. Adaptive Control of Linear Hyperbolic PDEs is of value to researchers and practitioners in applied mathematics, engineering and physics; it contains a rich set of adaptive control designs, including mathematical proofs and simulation demonstrations. The book is also of interest to students looking to expand their knowledge of hyperbolic PDEs.
Delay Adaptive Linear Control
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Author : Yang Zhu
language : en
Publisher: Princeton University Press
Release Date : 2020-04-28
Delay Adaptive Linear Control written by Yang Zhu and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-28 with Mathematics categories.
Actuator and sensor delays are among the most common dynamic phenomena in engineering practice, and when disregarded, they render controlled systems unstable. Over the past sixty years, predictor feedback has been a key tool for compensating such delays, but conventional predictor feedback algorithms assume that the delays and other parameters of a given system are known. When incorrect parameter values are used in the predictor, the resulting controller may be as destabilizing as without the delay compensation. Delay-Adaptive Linear Control develops adaptive predictor feedback algorithms equipped with online estimators of unknown delays and other parameters. Such estimators are designed as nonlinear differential equations, which dynamically adjust the parameters of the predictor. The design and analysis of the adaptive predictors involves a Lyapunov stability study of systems whose dimension is infinite, because of the delays, and nonlinear, because of the parameter estimators. This comprehensive book solves adaptive delay compensation problems for systems with single and multiple inputs/outputs, unknown and distinct delays in different input channels, unknown delay kernels, unknown plant parameters, unmeasurable finite-dimensional plant states, and unmeasurable infinite-dimensional actuator states. Presenting breakthroughs in adaptive control and control of delay systems, Delay-Adaptive Linear Control offers powerful new tools for the control engineer and the mathematician.
Control Strategy For Time Delay Systems
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Author : Mohammad-Hassan Khooban
language : en
Publisher: Academic Press
Release Date : 2020-11-27
Control Strategy For Time Delay Systems written by Mohammad-Hassan Khooban and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-27 with Technology & Engineering categories.
Since delays are present in 99% of industrial processes, Control Strategy for Time-delay Systems covers all the important features of real-world practical applications which will be valuable to practicing engineers and specialists The book presents the views of the editors on promising research directions and future industrial applications in this area. Although the fundamentals of time-delay systems are discussed, the book focuses on the advanced modelling and control of such systems and will provide the analysis and test (or simulation) results of nearly every technique described in the book For this purpose, highly complex models are introduced to ?describe the mentioned new applications which are characterized by ?time-varying delays with intermittent and stochastic nature, several types of nonlinearities, and the presence ?of different time-scales. Researchers, practitioners and PhD students will gain insights into the prevailing trends in design and operation of real-time control systems, reviewing the shortcomings and future developments concerning the practical system issues such as standardization, protection and design.
Delay Adaptive Linear Control
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Author : Yang Zhu
language : en
Publisher: Princeton University Press
Release Date : 2020-04-28
Delay Adaptive Linear Control written by Yang Zhu and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-28 with Mathematics categories.
Basic predictor feedback for single-input systems -- Basic idea of adaptive control for single-input systems -- Single-input systems with full relative degree -- Single-input systems with arbitrary relative degree -- Exact predictor feedback for multi-input systems -- Full-state feedback of uncertain multi-input systems -- Output feedback of uncertain multi-input systems -- Output feedback of systems with uncertain delays, parameters and ODE state -- Predictor feedback for uncertainty-free systems -- Predictor feedback of uncertain single-input systems -- Predictor feedback of uncertain multi-input systems.
Recent Results On Nonlinear Delay Control Systems
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Author : Iasson Karafyllis
language : en
Publisher: Springer
Release Date : 2015-07-15
Recent Results On Nonlinear Delay Control Systems written by Iasson Karafyllis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-15 with Technology & Engineering categories.
This volume collects recent advances in nonlinear delay systems, with an emphasis on constructive generalized Lyapunov and predictive approaches that certify stability properties. The book is written by experts in the field and includes two chapters by Miroslav Krstic, to whom this volume is dedicated. This volume is suitable for all researchers in mathematics and engineering who deal with nonlinear delay control problems and students who would like to understand the current state of the art in the control of nonlinear delay systems.
Control Of Partial Differential Equations
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Author : Jean-michel Coron
language : en
Publisher: World Scientific
Release Date : 2023-04-11
Control Of Partial Differential Equations written by Jean-michel Coron and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-11 with Mathematics categories.
This book is mainly a collection of lecture notes for the 2021 LIASFMA International Graduate School on Applied Mathematics. It provides the readers some important results on the theory, the methods, and the application in the field of 'Control of Partial Differential Equations'. It is useful for researchers and graduate students in mathematics or control theory, and for mathematicians or engineers with an interest in control systems governed by partial differential equations.