Optimization Based Feedback Control Of Nonlinear Systems Subject To Input Constraints
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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
Nonlinear Control Systems Ii
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Author : Alberto Isidori
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Control Systems Ii written by Alberto Isidori 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 Technology & Engineering categories.
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.
How Can Robust Control Of Nonlinear Systems Be Achieved Examining Optimization Techniques
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Author : Bhawna Tandon
language : en
Publisher: GRIN Verlag
Release Date : 2019-10-18
How Can Robust Control Of Nonlinear Systems Be Achieved Examining Optimization Techniques written by Bhawna Tandon and has been published by GRIN Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-18 with Technology & Engineering categories.
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.
Neural Network Based Adaptive Control Of Uncertain Nonlinear Systems
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Author : Kasra Esfandiari
language : en
Publisher: Springer Nature
Release Date : 2021-06-18
Neural Network Based Adaptive Control Of Uncertain Nonlinear Systems written by Kasra Esfandiari and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-18 with Technology & Engineering categories.
The focus of this book is the application of artificial neural networks in uncertain dynamical systems. It explains how to use neural networks in concert with adaptive techniques for system identification, state estimation, and control problems. The authors begin with a brief historical overview of adaptive control, followed by a review of mathematical preliminaries. In the subsequent chapters, they present several neural network-based control schemes. Each chapter starts with a concise introduction to the problem under study, and a neural network-based control strategy is designed for the simplest case scenario. After these designs are discussed, different practical limitations (i.e., saturation constraints and unavailability of all system states) are gradually added, and other control schemes are developed based on the primary scenario. Through these exercises, the authors present structures that not only provide mathematical tools for navigating control problems, but also supply solutions that are pertinent to real-life systems.
Nonlinear H2 H Infinity Constrained Feedback Control
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Author : Murad Abu-Khalaf
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-08-02
Nonlinear H2 H Infinity Constrained Feedback Control written by Murad Abu-Khalaf 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 2006-08-02 with Technology & Engineering categories.
This book provides techniques to produce robust, stable and useable solutions to problems of H-infinity and H2 control in high-performance, non-linear systems for the first time. The book is of importance to control designers working in a variety of industrial systems. Case studies are given and the design of nonlinear control systems of the same caliber as those obtained in recent years using linear optimal and bounded-norm designs is explained.
Stabilization Of Nonlinear Systems Using Receding Horizon Control Schemes
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Author : Mazen Alamir
language : en
Publisher: Springer
Release Date : 2006-09-29
Stabilization Of Nonlinear Systems Using Receding Horizon Control Schemes written by Mazen Alamir and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-29 with Technology & Engineering categories.
While conceptually elegant, the generic formulations of nonlinear model predictive control are not ready to use for the stabilization of relatively fast systems. This book presents a successful approach to this problem based on a co-operation between structural considerations and on-line optimization. It also provides research showing how generic predictive control schemes can be extended from slow process-based systems to a variety of fast systems.
Nonlinear Control Systems
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Author : Alberto Isidori
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Nonlinear Control Systems written by Alberto Isidori 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 2013-04-17 with Computers categories.
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.
Nonlinear Control Systems
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Author : Alberto Isidori
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Nonlinear Control Systems written by Alberto Isidori 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 2013-04-17 with Technology & Engineering categories.
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.
Feedback Control Nonlinear Systems And Complexity
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Author : George Zames
language : en
Publisher: Springer
Release Date : 1995
Feedback Control Nonlinear Systems And Complexity written by George Zames and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Computers categories.
This volume is the proceedings of a conference held May 6 and 7, 1994 at McGill University in Montreal in honour of Professor George on the occasion of his 60th birthday. He has devoted most of his professional life to the subject of feedback control. Invited speakers were internationally prominent researchers from the USA, Canada, UK and the Netherlands. Their papers cover various aspects of linear multivariable feedback control, nonlinear systems and the complexity of systems.
Nonlinear Model Predictive Control
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Author : Frank Allgöwer
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Nonlinear Model Predictive Control written by Frank Allgöwer and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
During the past decade model predictive control (MPC), also referred to as receding horizon control or moving horizon control, has become the preferred control strategy for quite a number of industrial processes. There have been many significant advances in this area over the past years, one of the most important ones being its extension to nonlinear systems. This book gives an up-to-date assessment of the current state of the art in the new field of nonlinear model predictive control (NMPC). The main topic areas that appear to be of central importance for NMPC are covered, namely receding horizon control theory, modeling for NMPC, computational aspects of on-line optimization and application issues. The book consists of selected papers presented at the International Symposium on Nonlinear Model Predictive Control – Assessment and Future Directions, which took place from June 3 to 5, 1998, in Ascona, Switzerland. The book is geared towards researchers and practitioners in the area of control engineering and control theory. It is also suited for postgraduate students as the book contains several overview articles that give a tutorial introduction into the various aspects of nonlinear model predictive control, including systems theory, computations, modeling and applications.