Finite-Time Stability Tools for Control and Estimation
Finite-Time Stability Tools for Control and Estimation

Author: Denis Efimov

Publisher:

Published: 2021-12-09

Total Pages: 214

ISBN-13: 9781680839265

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This monograph presents some existing and new results on analysis and design of finite-time and fixed-time converging systems. Two main groups of approaches for analysis/synthesis of this kind of convergence, Lyapunov functions and the theory of homogeneous systems, are considered.The authors focus on the dynamics described by ordinary differential equations, time-delay models and partial differential equations. Some popular control and estimation algorithms, which possess accelerated converge rates, are also reviewed. Finally, the issues of discretization of finite-/fixed-time converging systems are discussed.Divided into 3 parts, this monograph provides the reader with a complete and accessible review of the topic. In the first part, the definitions of the different finite-/fixed-time stability properties are given together with their characterizations via the Lyapunov function approach. In the second part, several stabilization algorithms for linear and nonlinear systems are formalized, which are based on the implicit Lyapunov function approach. In the third part, the issues of discretization of finite-/fixed-time stable systems are discussed, with a special attention to the solutions obtained with the implicit Lyapunov function method. Finally, the accelerated converge concepts are presented for systems described by time-delay and partial differential equations.This monograph is an excellent introduction to the complex field of Finite-Time Stability Tools. It enables the reader to synthesize the important concepts and further their own research in the area.

FINITE-TIME STABILITY TOOLS FOR CONTROL AND ESTIMATION
FINITE-TIME STABILITY TOOLS FOR CONTROL AND ESTIMATION

Author: DENIS EFIMOV; ANDREY POLYAKOV.

Publisher:

Published: 2021

Total Pages:

ISBN-13: 9781680839272

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This monograph presents some existing and new results on analysis and design of finite-time and fixed-time converging systems. Two main groups of approaches for analysis/synthesis of this kind of convergence, Lyapunov functions and the theory of homogeneous systems, are considered. The authors focus on the dynamics described by ordinary differential equations, time-delay models and partial differential equations. Some popular control and estimation algorithms, which possess accelerated converge rates, are also reviewed. Finally, the issues of discretization of finite-/fixed-time converging systems are discussed. Divided into 3 parts, this monograph provides the reader with a complete and accessible review of the topic. In the first part, the definitions of the different finite-/fixed-time stability properties are given together with their characterizations via the Lyapunov function approach. In the second part, several stabilization algorithms for linear and nonlinear systems are formalized, which are based on the implicit Lyapunov function approach. In the third part, the issues of discretization of finite-/fixed-time stable systems are discussed, with a special attention to the solutions obtained with the implicit Lyapunov function method. Finally, the accelerated converge concepts are presented for systems described by time-delay and partial differential equations. This monograph is an excellent introduction to the complex field of Finite-Time Stability Tools. It enables the reader to synthesize the important concepts and further their own research in the area.

Finite-Time Stability and Control
Finite-Time Stability and Control

Author: Francesco Amato

Publisher: Springer

Published: 2013-12-03

Total Pages: 147

ISBN-13: 1447156641

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Finite-time stability (FTS) is a more practical concept than classical Lyapunov stability, useful for checking whether the state trajectories of a system remain within pre-specified bounds over a finite time interval. In a linear systems framework, FTS problems can be cast as convex optimization problems and solved by the use of effective off-the-shelf computational tools such as LMI solvers. Finite-time Stability and Control exploits this benefit to present the practical applications of FTS and finite-time control-theoretical results to various engineering fields. The text is divided into two parts: · linear systems; and · hybrid systems. The building of practical motivating examples helps the reader to understand the methods presented. Finite-time Stability and Control is addressed to academic researchers and to engineers working in the field of robust process control. Instructors teaching graduate courses in advanced control will also find parts of this book useful for their courses.

Finite-Time Stability: An Input-Output Approach
Finite-Time Stability: An Input-Output Approach

Author: Francesco Amato

Publisher: John Wiley & Sons

Published: 2018-10-08

Total Pages: 184

ISBN-13: 1119140528

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Systematically presents the input-output finite-time stability (IO-FTS) analysis of dynamical systems, covering issues of analysis, design and robustness The interest in finite-time control has continuously grown in the last fifteen years. This book systematically presents the input-output finite-time stability (IO-FTS) analysis of dynamical systems, with specific reference to linear time-varying systems and hybrid systems. It discusses analysis, design and robustness issues, and includes applications to real world engineering problems. While classical FTS has an important theoretical significance, IO-FTS is a more practical concept, which is more suitable for real engineering applications, the goal of the research on this topic in the coming years. Key features: Includes applications to real world engineering problems. Input-output finite-time stability (IO-FTS) is a practical concept, useful to study the behavior of a dynamical system within a finite interval of time. Computationally tractable conditions are provided that render the technique applicable to time-invariant as well as time varying and impulsive (i.e. switching) systems. The LMIs formulation allows mixing the IO-FTS approach with existing control techniques (e. g. H∞ control, optimal control, pole placement, etc.). This book is essential reading for university researchers as well as post-graduate engineers practicing in the field of robust process control in research centers and industries. Topics dealt with in the book could also be taught at the level of advanced control courses for graduate students in the department of electrical and computer engineering, mechanical engineering, aeronautics and astronautics, and applied mathematics.

Constrained Control and Estimation
Constrained Control and Estimation

Author: Graham Goodwin

Publisher: Springer Science & Business Media

Published: 2006-03-30

Total Pages: 415

ISBN-13: 184628063X

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Recent developments in constrained control and estimation have created a need for this comprehensive introduction to the underlying fundamental principles. These advances have significantly broadened the realm of application of constrained control. - Using the principal tools of prediction and optimisation, examples of how to deal with constraints are given, placing emphasis on model predictive control. - New results combine a number of methods in a unique way, enabling you to build on your background in estimation theory, linear control, stability theory and state-space methods. - Companion web site, continually updated by the authors. Easy to read and at the same time containing a high level of technical detail, this self-contained, new approach to methods for constrained control in design will give you a full understanding of the subject.

Control and Inverse Problems
Control and Inverse Problems

Author: Kaïs Ammari

Publisher: Springer Nature

Published: 2023-09-26

Total Pages: 276

ISBN-13: 3031356756

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This volume presents a timely overview of control theory and inverse problems, and highlights recent advances in these active research areas. The chapters are based on talks given at the spring school "Control & Inverse Problems” held in Monastir, Tunisia in May 2022. In addition to providing a snapshot of these two areas, chapters also highlight breakthroughs on more specific topics, such as: Controllability of dynamical systems Information transfer in multiplier equations Nonparametric instrumental regression Control of chained systems The damped wave equation Control and Inverse Problems will be a valuable resource for both established researchers as well as more junior members of the community.

Current Trends in Nonlinear Systems and Control
Current Trends in Nonlinear Systems and Control

Author: Laura Menini

Publisher: Springer Science & Business Media

Published: 2006-09-13

Total Pages: 557

ISBN-13: 0817644709

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This volume is an outgrowth of the workshop "Applications of Advanced Control Theory to Robotics and Automation, "organized in honor of the 70th birthdays of Petar V. Kokotovic and Salvatore (Turi) Nicosia. Both Petar and Turi have carried out distinguished work in the control community and have long been recognized as mentors, as well as experts and pioneers in the field of automatic control, covering many topics in control theory and several different applications. The variety of their research is reflected in this book, which includes contributions ranging from mathematics to laboratory experiments. The scope of the work is very broad, and although each chapter is self-contained, the book has been organized into thematically related chapters, which in some cases, suggest to the reader a convenient reading sequence. The great variety of topics covered and the almost tutorial writing style used by many of the authors will make this book suitable for both experts in the control field and young researchers who seek a more intuitive understanding of these relevant topics in the field.

Generalized Homogeneity in Systems and Control
Generalized Homogeneity in Systems and Control

Author: Andrey Polyakov

Publisher: Springer Nature

Published: 2020-02-05

Total Pages: 454

ISBN-13: 3030384497

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This monograph introduces the theory of generalized homogeneous systems governed by differential equations in both Euclidean (finite-dimensional) and Banach/Hilbert (infinite-dimensional) spaces. It develops methods of stability and robustness analysis, control design, state estimation and discretization of homogeneous control systems. Generalized Homogeneity in Systems and Control is structured in two parts. Part I discusses various models of control systems and related tools for their analysis, including Lyapunov functions. Part II deals with the analysis and design of homogeneous control systems. Some of the key features of the text include: mathematical models of dynamical systems in finite-dimensional and infinite-dimensional spaces; the theory of linear dilations in Banach spaces; homogeneous control and estimation; simple methods for an "upgrade" of existing linear control laws; numerical schemes for a consistent digital implementation of homogeneous algorithms; and experiments confirming an improvement of PID controllers. The advanced mathematical material will be of interest to researchers, mathematicians working in control theory and mathematically oriented control engineers.

Prescribed-Time Stabilization and Estimation for Linear Systems with Applications in Tactical Missile Guidance
Prescribed-Time Stabilization and Estimation for Linear Systems with Applications in Tactical Missile Guidance

Author: John Charles Holloway

Publisher:

Published: 2018

Total Pages: 272

ISBN-13:

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Motivated by tactical missile guidance, in which there exists a short, finite amount of time to intercept a moving target, we introduce a new approach to stabilization and estimation in finite time which allows the user to prescribe the time by which the estimation and control objectives will be achieved. We accomplish this by employing time-varying feedback gains which tend to infinity as time approaches the prescribed time. Remarkably, despite the gains going to infinity, the overall control inputs and output estimation error injections remain finite, thereby allowing for potential use in real-world finite-time control applications such as tactical missile guidance. The first step in the design process involves extending existing stability concepts for nonlinear systems by introducing new definitions for finite-time stability using class K and class KL functions. This is done by compressing the usual infinite time interval to a finite one through the use of a time-varying, monotonic scaling function which tends to infinity as time approaches the prescribed time. Then, time-varying state coordinate transformations are used to design two feedback controllers for nonlinear systems in the normal form which stabilize the state in a finite time that is independent of initial conditions and freely prescribed by the user. The first controller is appropriate for systems having no uncertainties, while the second is intended for systems having matched uncertainties and possibly unknown control input coefficient. Prescribed-time observers for linear systems in the observer canonical form are then introduced using a similar time-varying state coordinate transformation design, resulting in observers akin to the Luenberger observer but with time-varying gains that tend to infinity as time approaches the prescribed time. Then, the prescribed-time uncertainty-free controller and prescribed-time observer are combined, and it is shown that a finite-time separation principle exists between the controller and the observer. The presentation is concluded with a series of examples in which the new prescribed-time controllers and observers are applied to provide new solutions to canonical problems in tactical missile guidance.