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Author: Bhawna Tandon
Publisher: GRIN Verlag
ISBN: 3346038653
Category : Technology & Engineering
Languages : en
Pages : 170
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Book Description
Doctoral Thesis / Dissertation from the year 2019 in the subject Engineering - General, Basics, grade: A.00, , language: English, abstract: The following text examines the questions, how nonlinear system can better be controlled by new optimisation techniques such as feedback linearization. Due to the inevitable nonlinearities in real systems, several nonlinear control methods like feedback linearization, sliding mode control, backstepping approach and further modes are described in detail in the literature. Due to limitations in application of well known classical methods, researchers have struggled for decades to realize robust and practical solutions for nonlinear systems by proposing different approaches or improving classical control methods. The feedback linearization approach is a control method which employs feedback to stabilize systems containing nonlinearities. In order to accomplish this, it assumes perfect knowledge of the system model to linearize the input-output relationship. In the absence of perfect system knowledge, modelling errors inevitably affect the performanceof the feedback controller. Many researchers have come up with a new form of feedback linearization, called robust feedback. This method gives a linearizing control law that transforms the nonlinear system into its linear approximation around an operating point. Thus, it causes only a small transformation in the natural behavior of the system, which is desired in order to obtain robustness. The controllers are required to provide various time domain and frequency domain performances while maintaining sufficient stability robustness. In this regard, the evolutionary optimization techniques provide better option as these are probabilistic search procedures and facilitate inclusion of wide variety of time and frequency domain performance functionals in the objective functions. A significant scope of work remains to be done which provides motivation for the research in the design of robust controllers using evolutionary optimization. Also, emerging techniques using LMI also find potential in controller design for feedback linearized systems.The thrust of the study here is to design robust controllers for nonlinear systems using Evolutionary optimization and LMI. Furthermore, latest control methods for nonlinear system have been studied, deeply, in this thesis. Combining feedback linearization with non linear disturbance observer based control (NDOBC) obtains promising disturbance rejection and reference tracking performance as compared to other robust control methods.
Author: Bhawna Tandon
Publisher: GRIN Verlag
ISBN: 3346038653
Category : Technology & Engineering
Languages : en
Pages : 170
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Book Description
Doctoral Thesis / Dissertation from the year 2019 in the subject Engineering - General, Basics, grade: A.00, , language: English, abstract: The following text examines the questions, how nonlinear system can better be controlled by new optimisation techniques such as feedback linearization. Due to the inevitable nonlinearities in real systems, several nonlinear control methods like feedback linearization, sliding mode control, backstepping approach and further modes are described in detail in the literature. Due to limitations in application of well known classical methods, researchers have struggled for decades to realize robust and practical solutions for nonlinear systems by proposing different approaches or improving classical control methods. The feedback linearization approach is a control method which employs feedback to stabilize systems containing nonlinearities. In order to accomplish this, it assumes perfect knowledge of the system model to linearize the input-output relationship. In the absence of perfect system knowledge, modelling errors inevitably affect the performanceof the feedback controller. Many researchers have come up with a new form of feedback linearization, called robust feedback. This method gives a linearizing control law that transforms the nonlinear system into its linear approximation around an operating point. Thus, it causes only a small transformation in the natural behavior of the system, which is desired in order to obtain robustness. The controllers are required to provide various time domain and frequency domain performances while maintaining sufficient stability robustness. In this regard, the evolutionary optimization techniques provide better option as these are probabilistic search procedures and facilitate inclusion of wide variety of time and frequency domain performance functionals in the objective functions. A significant scope of work remains to be done which provides motivation for the research in the design of robust controllers using evolutionary optimization. Also, emerging techniques using LMI also find potential in controller design for feedback linearized systems.The thrust of the study here is to design robust controllers for nonlinear systems using Evolutionary optimization and LMI. Furthermore, latest control methods for nonlinear system have been studied, deeply, in this thesis. Combining feedback linearization with non linear disturbance observer based control (NDOBC) obtains promising disturbance rejection and reference tracking performance as compared to other robust control methods.
Author: Stefan LeBel
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Thomas L. Vincent
Publisher: John Wiley & Sons
ISBN: 9780471042358
Category : Science
Languages : en
Pages : 584
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Book Description
Designed for one-semester introductory senior-or graduate-level course, the authors provide the student with an introduction of analysis techniques used in the design of nonlinear and optimal feedback control systems. There is special emphasis on the fundamental topics of stability, controllability, and optimality, and on the corresponding geometry associated with these topics. Each chapter contains several examples and a variety of exercises.
Author: Alberto Isidori
Publisher: Springer Science & Business Media
ISBN: 1447105494
Category : Technology & Engineering
Languages : en
Pages : 300
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Book Description
This eagerly awaited follow-up to Nonlinear Control Systems incorporates recent advances in the design of feedback laws, for the purpose of globally stabilizing nonlinear systems via state or output feedback. The author is one of the most prominent researchers in the field.
Author: Dimitrios Stylianos Parsinas Pylorof
Publisher:
ISBN:
Category :
Languages : en
Pages : 266
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Book Description
In this work, we are studying and solving feedback control problems for input constrained nonlinear systems under the influence of uncertainty. Our results are developed by fusing fundamental Lyapunov stability concepts with tools and techniques from the field of convex optimization that enable the derivation of computationally efficient control laws accompanied by robust stabilization guarantees. When a nonlinear control system is subject to input constraints, a critical aspect of the stabilization problem with simple control laws based on a particular Control Lyapunov Function (CLF) is to characterize a subset of the state space starting from where stabilization to the origin is guaranteed. We consider polynomial systems which are affine in a control input constrained in a convex and compact polytope. We propose two alternative analysis methods that ultimately yield sufficient conditions for asymptotic stabilization under such input constraints and provide an estimate of the stabilization set for the system and the given CLF. Both methods relax the problem to the solution of Sum-of-Squares programs, which nominally can be cast as Semidefinite Programs that are solvable with interior point algorithms. Given a particular CLF, it is also possible to sequentially optimize over its coefficients to the end of reshaping or enlarging the stabilization set, and thus, favorably altering the set of initial conditions from where the control objectives can be attained. A class of constrained control laws based on a particular CLF is shown to attain values equal to the minimizer of a Quadratic Program (QP), which is guaranteed to remain feasible along any closed loop trajectory emanating from the stabilization set. The input constraints are always respected and the closed loop system is rendered asymptotically stable. Additionally, such a QP is of a rather low dimension and can be solved efficiently, enabling the embedded implementation of the proposed control laws even on resource-constrained computational platforms. For the case of systems subject to unknown, bounded uncertainties that enter the dynamics in an affine way, the aforedescribed results are extended to provide robust stabilization subject to input constraints. With the proposed methods, the min-max conditions typically encountered in Lyapunov methods with Robust CLFs (RCLFs) for such systems are handled in both the (R)CLF analysis and the feedback control problem. Therefore, one can estimate a subset of the robust stabilization set with SOS programming and, subsequently, calculate - online - the stabilizing control inputs using state feedback to render the system robustly practically stable. An often encountered challenge in nonlinear control design and implementation is the large dimension of the underlying system, often resulting from the interconnection of multiple subsystems which interact with each other. The concept of Vector (Control) Lyapunov functions allows studying or warranting the applicable stability notion by focusing at the subsystem level and the respective subsystem-to-subsystem interactions. We are leveraging the premise of VCLF methods with our results on the robust stabilization problem to enable the solution of the input constrained robust stabilization problem for large scale systems, either in a distributed or a decentralized way (or in a combination of both), depending on whether state information is exchanged between interacting subsystems or not. Lastly, we examine how uncertainty in the measurements of the system can affect the stabilization problem under input constraints. We propose a control framework with which one can steer a system to a neighborhood of the origin using only imperfect state feedback. The latter is achieved by enforcing a causality relationship between stabilizing the system from the point of view of an imperfect feedback control law and stabilizing the actual system. Ultimately, we use control laws based, again, on the minimizer of simple QPs, to provingly achieve the robust stabilization objective in a subset of the measurement space which is characterized by solving a sequence of SOS programming problems. For the case where only imperfect measurements either of a subset of the state vector of the system or of a linear combination of state vector components are available, we propose an extension of Lyapunov-based nonlinear observer design results from the literature to account for uncertainty in the dynamics and the measurement equation. The robust observer synthesis process takes place through SOS programming and produces observers with explicit performance guarantees with regards to the behavior of the state determination error. The factors considered in this work are relevant to contemporary safety-critical control applications; nonlinearity, input constraints, uncertainty, and the need for embeddability and low footprint implementation are ubiquitous in control problems across fields ranging from robotics to industrial engineering, space exploration and cyber-physical systems. The proposed methods aim to collectively provide a theoretically sound, algorithmically implementable and practically useful framework to study and tackle challenging control problems
Author: Alberto Isidori
Publisher: Springer Science & Business Media
ISBN: 3662025817
Category : Computers
Languages : en
Pages : 487
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Book Description
The purpose of this book is to present a self-contained description of the fundamentals of the theory of nonlinear control systems, with special emphasis on the differential geometric approach. The book is intended as a graduate text as well as a reference to scientists and engineers involved in the analysis and design of feedback systems. The first version of this book was written in 1983, while I was teaching at the Department of Systems Science and Mathematics at Washington University in St. Louis. This new edition integrates my subsequent teaching experience gained at the University of Illinois in Urbana-Champaign in 1987, at the Carl Cranz Gesellschaft in Oberpfaffenhofen in 1987, at the University of California in Berkeley in 1988. In addition to a major rearrangement of the last two Chapters of the first version, this new edition incorporates two additional Chapters at a more elementary level and an exposition of some relevant research findings which have occurred since 1985. In the past few years differential geometry has proved to be an effective means of analysis and design of nonlinear control systems as it was in the past for the Laplace transform, complex variable theory and linear algebra in relation to linear systems. Synthesis problems of longstanding interest like disturbance decoupling, noninteracting control, output regulation, and the shaping of the input-output response, can be dealt with relative ease, on the basis of mathematical concepts that can be easily acquired by a control scientist.
Author: William M. McEneaney
Publisher: Springer Science & Business Media
ISBN: 0817644539
Category : Mathematics
Languages : en
Pages : 252
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Book Description
The central focus of this book is the control of continuous-time/continuous-space nonlinear systems. Using new techniques that employ the max-plus algebra, the author addresses several classes of nonlinear control problems, including nonlinear optimal control problems and nonlinear robust/H-infinity control and estimation problems. Several numerical techniques are employed, including a max-plus eigenvector approach and an approach that avoids the curse-of-dimensionality. The max-plus-based methods examined in this work belong to an entirely new class of numerical methods for the solution of nonlinear control problems and their associated Hamilton–Jacobi–Bellman (HJB) PDEs; these methods are not equivalent to either of the more commonly used finite element or characteristic approaches. Max-Plus Methods for Nonlinear Control and Estimation will be of interest to applied mathematicians, engineers, and graduate students interested in the control of nonlinear systems through the implementation of recently developed numerical methods.
Author: Aziz Belmiloudi
Publisher: Springer Science & Business Media
ISBN: 1848003447
Category : Technology & Engineering
Languages : en
Pages : 509
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Book Description
Stabilization, Optimal and Robust Control develops robust control of infinite-dimensional dynamical systems derived from time-dependent coupled PDEs associated with boundary-value problems. Rigorous analysis takes into account nonlinear system dynamics, evolutionary and coupled PDE behaviour and the selection of function spaces in terms of solvability and model quality. Mathematical foundations are provided so that the book remains accessible to the non-control-specialist. Following chapters giving a general view of convex analysis and optimization and robust and optimal control, problems arising in fluid mechanical, biological and materials scientific systems are laid out in detail. The combination of mathematical fundamentals with application of current interest will make this book of much interest to researchers and graduate students looking at complex problems in mathematics, physics and biology as well as to control theorists.
Author: Alberto Isidori
Publisher: Springer Science & Business Media
ISBN: 9783540199168
Category : Technology & Engineering
Languages : en
Pages : 580
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Book Description
The purpose of this book is to present a self-contained description of the fun damentals of the theory of nonlinear control systems, with special emphasis on the differential geometric approach. The book is intended as a graduate text as weil as a reference to scientists and engineers involved in the analysis and design of feedback systems. The first version of this book was written in 1983, while I was teach ing at the Department of Systems Science and Mathematics at Washington University in St. Louis. This new edition integrates my subsequent teaching experience gained at the University of Illinois in Urbana-Champaign in 1987, at the Carl-Cranz Gesellschaft in Oberpfaffenhofen in 1987, at the University of California in Berkeley in 1988. In addition to a major rearrangement of the last two Chapters of the first version, this new edition incorporates two additional Chapters at a more elementary level and an exposition of some relevant research findings which have occurred since 1985.
Author: Randy A. Freeman
Publisher: Birkhauser
ISBN: 9783764339302
Category : Doğrusal olmayan kontrol teorisi
Languages : en
Pages : 257
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Book Description
