Stabilization Problems With Constraints
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Stabilization Problems With Constraints
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Author : Vladimir A Bushenkov
language : en
Publisher: CRC Press
Release Date : 2021-12-17
Stabilization Problems With Constraints written by Vladimir A Bushenkov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-17 with Science categories.
Presents and demonstrates stabilizer design techniques that can be used to solve stabilization problems with constraints. These methods have their origins in convex programming and stability theory. However, to provide a practical capability in stabilizer design, the methods are tailored to the special features and needs of this field. Hence, the main emphasis of this book is on the methods of stabilization, rather than optimization and stability theory. The text is divided into three parts. Part I contains some background material. Part II is devoted to behavior of control systems, taking examples from mechanics to illustrate the theory. Finally, Part III deals with nonlocal stabilization problems, including a study of the global stabilization problem.
Stabilization Problems With Constraints
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Author : Vladimir A Bushenkov
language : en
Publisher: CRC Press
Release Date : 1998-04-29
Stabilization Problems With Constraints written by Vladimir A Bushenkov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-04-29 with Science categories.
Presents and demonstrates stabilizer design techniques that can be used to solve stabilization problems with constraints. These methods have their origins in convex programming and stability theory. However, to provide a practical capability in stabilizer design, the methods are tailored to the special features and needs of this field. Hence, the main emphasis of this book is on the methods of stabilization, rather than optimization and stability theory. The text is divided into three parts. Part I contains some background material. Part II is devoted to behavior of control systems, taking examples from mechanics to illustrate the theory. Finally, Part III deals with nonlocal stabilization problems, including a study of the global stabilization problem.
Topics In Stabilization Under Constraints And Synchronization Problems
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Author : Xu Wang
language : en
Publisher:
Release Date : 2012
Topics In Stabilization Under Constraints And Synchronization Problems written by Xu Wang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with categories.
When the issues related to internal stabilization are resolved, the research is directed to simultaneous stabilization problems. The focus here is linear system subject to input saturation. In the case where disturbances that are additive to the input, we complement the existing results in the literature by solving the simultaneous stabilization problems for discrete-time linear systems subject to input saturation. Then attention is paid to non-input-additive disturbances. This research is carried out using a progressive approach. The results are obtained and generalized from a simple double integrator to the most general linear systems. It is found that the simultaneous stabilization problems are solvable if the disturbances do not contained large frequency component corresponding to the open-loop eigenvalues on the stability margin. For those disturbances that meet this criterion, dynamical feedback controller can be constructed to achieve simultaneous stabilization.
Control Of Linear Systems Subjet To Constraints
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Author : Guoyong Shi
language : en
Publisher:
Release Date : 2002
Control Of Linear Systems Subjet To Constraints written by Guoyong Shi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Linear systems categories.
Optimal Structural Design Under Stability Constraints
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Author : Antoni Gajewski
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Optimal Structural Design Under Stability Constraints written by Antoni Gajewski 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 first optimal design problem for an elastic column subject to buckling was formulated by Lagrange over 200 years ago. However, rapid development of structural optimization under stability constraints occurred only in the last twenty years. In numerous optimal structural design problems the stability phenomenon becomes one of the most important factors, particularly for slender and thin-walled elements of aerospace structures, ships, precision machines, tall buildings etc. In engineering practice stability constraints appear more often than it might be expected; even when designing a simple beam of constant width and variable depth, the width - if regarded as a design variable - is finally determined by a stability constraint (lateral stability). Mathematically, optimal structural design under stability constraints usually leads to optimization with respect to eigenvalues, but some cases fall even beyond this type of problems. A total of over 70 books has been devoted to structural optimization as yet, but none of them has treated stability constraints in a sufficiently broad and comprehensive manner. The purpose of the present book is to fill this gap. The contents include a discussion of the basic structural stability and structural optimization problems and the pertinent solution methods, followed by a systematic review of solutions obtained for columns, arches, bar systems, plates, shells and thin-walled bars. A unified approach based on Pontryagin's maximum principle is employed inasmuch as possible, at least to problems of columns, arches and plates. Parametric optimization is discussed as well.
Internal And External Stabilization Of Linear Systems With Constraints
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Author : Ali Saberi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-06-21
Internal And External Stabilization Of Linear Systems With Constraints written by Ali Saberi 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 2012-06-21 with Science categories.
Unifying two decades of research, this book is the first to establish a comprehensive foundation for a systematic analysis and design of linear systems with general state and input constraints. For such systems, which can be used as models for most nonlinear systems, the issues of stability, controller design, additonal constraints, and satisfactory performance are addressed. The book is an excellent reference for practicing engineers, graduate students, and researchers in control systems theory and design. It may also serve as an advanced graduate text for a course or a seminar in nonlinear control systems theory and design in applied mathematics or engineering departments. Minimal prerequisites include a first graduate course in state-space methods as well as a first course in control systems design.
Internal And External Stabilization Of Linear Systems With Constraints
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Author : Springer
language : en
Publisher:
Release Date : 2012-08-31
Internal And External Stabilization Of Linear Systems With Constraints written by Springer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-31 with categories.
Stability Constrained Optimization For Modern Power System Operation And Planning
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Author : Yan Xu
language : en
Publisher: John Wiley & Sons
Release Date : 2023-06-27
Stability Constrained Optimization For Modern Power System Operation And Planning written by Yan Xu and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-27 with Technology & Engineering categories.
Stability-Constrained Optimization for Modern Power System Operation and Planning Comprehensive treatment of an aspect of stability constrained operations and planning, including the latest research and engineering practices Stability-Constrained Optimization for Modern Power System Operation and Planning focuses on the subject of power system stability. Unlike other books in this field, which focus mainly on the dynamic modeling, stability analysis, and controller design for power systems, this book is instead dedicated to stability-constrained optimization methodologies for power system stability enhancement, including transient stability-constrained power system dispatch and operational control, and voltage stability-constrained dynamic VAR Resources planning in the power grid. Authored by experts with established track records in both research and industry, Stability-Constrained Optimization for Modern Power System Operation and Planning covers three parts: Overview of power system stability, including definition, classification, phenomenon, mathematical models and analysis tools for stability assessment, as well as a review of recent large-scale blackouts in the world Transient stability-constrained optimal power flow (TSC-OPF) and transient stability constrained-unit commitment (TSC-UC) for power system dispatch and operational control, including a series of optimization model formulations, transient stability constraint construction and extraction methods, and efficient solution approaches Optimal planning of dynamic VAR Resources (such as STATCOM and SVC) in power system for voltage stability enhancement, including a set of voltage stability indices, candidate bus selection methods, multi-objective optimization model formulations, and high-quality solution approaches Stability-Constrained Optimization for Modern Power System Operation and Planning provides the latest research findings to scholars, researchers, and postgraduate students who are seeking optimization methodologies for power system stability enhancement, while also offering key practical methods to power system operators, planners, and optimization algorithm developers in the power industry.
Optimization Based Feedback Control Of Nonlinear Systems Subject To Input Constraints
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Author : Dimitrios Stylianos Parsinas Pylorof
language : en
Publisher:
Release Date : 2018
Optimization Based Feedback Control Of Nonlinear Systems Subject To Input Constraints written by Dimitrios Stylianos Parsinas Pylorof and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
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
Structural Optimization Under Stability And Vibration Constraints
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Author : M. Zyczkowski
language : en
Publisher: Springer
Release Date : 2014-05-04
Structural Optimization Under Stability And Vibration Constraints written by M. Zyczkowski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-04 with Technology & Engineering categories.
Optimal design of structures leads, as a rule, to slender and thin-walled shapes of the elements, and such elements are subject to the loss of stability. Hence the constraints of structural optimization usually include stability constraints, expressed by some eigenvalues. Optimal design under vibration constraints belongs also to optimization with respect to eigenvalues. The present volume gives a short introduction to structural optimization and then pays particular attention to multimodal optimization under stability and vibration constraints, both in elastic and inelastic range. One part is devoted to thin-walled bars optimized for interactive buckling with imperfections taken into account. The volume is of interest both to researchers and design engineers: it covers the most recent results of multimodal and interactive optimization, allowing for inelastic behaviour of structures, and the constraints discussed appear in almost all problems of engineering design.