Optimal Control Of Constrained Piecewise Affine Systems
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Optimal Control Of Constrained Piecewise Affine Systems
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Author : Frank Christophersen
language : en
Publisher: Springer
Release Date : 2009-09-02
Optimal Control Of Constrained Piecewise Affine Systems written by Frank Christophersen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-02 with Technology & Engineering categories.
One of the most important and challenging problems in control is the derivation of systematic tools for the computation of controllers for constrained nonlinear systems that can guarantee closed-loop stability, feasibility, and optimality with respect to some performance index. This book focuses on the efficient and systematic computation of closed-form optimal controllers for the powerful class of fast-sampled constrained piecewise affine systems. These systems may exhibit rather complex behavior and are equivalent to many other hybrid system formalisms (combining continuous-valued dynamics with logic rules) reported in the literature. Furthermore, piecewise affine systems are a useful modeling tool that can capture general nonlinearities (e.g. by local approximation), constraints, saturations, switches, and other hybrid modeling phenomena. The first part of the book presents an introduction to the mathematical and control theoretical background material needed for the full understanding of the book. The second part provides an in depth look at the computational and control theoretic properties of the controllers and part three presents different analysis and post-processing techniques.
Constrained Optimal Control
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Author : Thomas Besselmann
language : en
Publisher: CreateSpace
Release Date : 2010
Constrained Optimal Control written by Thomas Besselmann and has been published by CreateSpace this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Technology & Engineering categories.
The scope of this thesis lies in the field of constrained optimal control. More precisely, it is concerned with the constrained finite-time optimal control of two system classes: piecewise affine systems and linear parameter-varying systems. Firstly, constrained finite-time optimal control (CFTOC) of piecewise affine (PWA) systems is revisited. Since the actual computation of hybrid controllers as the explicit solution to parametric CFTOC problems for piecewise affine systems is already rather mature, this part deals with a post-processing algorithm. If the cost function of the CFTOC problem is quadratic, the optimization problem at hand is a parametric mixed-integer quadratic program, which can be solved by decomposing it into a number of quadratic programs. Thereby redundant regions are computed, which increase the storage demand and the online evaluation time of the resulting controller. We propose a post-processing algorithm for the removal of redundant regions. Furthermore, we examine the application of hybrid control methods to two systems: a mechanical system with backlash and autonomous vehicle steering. The second part of this thesis is devoted to constrained optimal control of linear parameter-varying (LPV) systems. A sequence of dynamic programming procedures is proposed, in order to solve constrained finite-time optimal control problems explicitly for LPV-A systems and for general LPV systems. Both cases of an arbitrarily varying scheduling parameter and a bounded rate of parameter variation are considered. Likewise, a procedure to solve the constrained time-optimal control problems is proposed, enabling a low-complexity alternative to explicit LPV-MPC with guaranteed stability. With these developments, explicit MPC schemes and explicit minimum-time MPC schemes are enriched by the class of LPV systems, increasing the possibilities of their application. Finally, we demonstrate an application of explicit LPV-MPC to autonomous vehicle steering.
Piecewise Affine Control Continuous Time Sampled Data And Networked Systems
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Author : Luis Rodrigues
language : en
Publisher: SIAM
Release Date : 2019-11-06
Piecewise Affine Control Continuous Time Sampled Data And Networked Systems written by Luis Rodrigues and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-06 with Mathematics categories.
Engineering systems operate through actuators, most of which will exhibit phenomena such as saturation or zones of no operation, commonly known as dead zones. These are examples of piecewise-affine characteristics, and they can have a considerable impact on the stability and performance of engineering systems. This book targets controller design for piecewise affine systems, fulfilling both stability and performance requirements. The authors present a unified computational methodology for the analysis and synthesis of piecewise affine controllers, taking an approach that is capable of handling sliding modes, sampled-data, and networked systems. They introduce algorithms that will be applicable to nonlinear systems approximated by piecewise affine systems, and they feature several examples from areas such as switching electronic circuits, autonomous vehicles, neural networks, and aerospace applications. Piecewise Affine Control: Continuous-Time, Sampled-Data, and Networked Systems is intended for graduate students, advanced senior undergraduate students, and researchers in academia and industry. It is also appropriate for engineers working on applications where switched linear and affine models are important.
Optimal Control Of Constrained Piecewise Affine Systems
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Author : Frank Christophersen
language : en
Publisher: Springer
Release Date : 2007-09-11
Optimal Control Of Constrained Piecewise Affine Systems written by Frank Christophersen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-09-11 with Technology & Engineering categories.
One of the most important and challenging problems in control is the derivation of systematic tools for the computation of controllers for constrained nonlinear systems that can guarantee closed-loop stability, feasibility, and optimality with respect to some performance index. This book focuses on the efficient and systematic computation of closed-form optimal controllers for the powerful class of fast-sampled constrained piecewise affine systems. These systems may exhibit rather complex behavior and are equivalent to many other hybrid system formalisms (combining continuous-valued dynamics with logic rules) reported in the literature. Furthermore, piecewise affine systems are a useful modeling tool that can capture general nonlinearities (e.g. by local approximation), constraints, saturations, switches, and other hybrid modeling phenomena. The first part of the book presents an introduction to the mathematical and control theoretical background material needed for the full understanding of the book. The second part provides an in depth look at the computational and control theoretic properties of the controllers and part three presents different analysis and post-processing techniques.
Constrained Optimal Control Of Linear And Hybrid Systems
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Author : Francesco Borrelli
language : en
Publisher: Springer
Release Date : 2003-09-04
Constrained Optimal Control Of Linear And Hybrid Systems written by Francesco Borrelli and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-09-04 with Mathematics categories.
Many practical control problems are dominated by characteristics such as state, input and operational constraints, alternations between different operating regimes, and the interaction of continuous-time and discrete event systems. At present no methodology is available to design controllers in a systematic manner for such systems. This book introduces a new design theory for controllers for such constrained and switching dynamical systems and leads to algorithms that systematically solve control synthesis problems. The first part is a self-contained introduction to multiparametric programming, which is the main technique used to study and compute state feedback optimal control laws. The book's main objective is to derive properties of the state feedback solution, as well as to obtain algorithms to compute it efficiently. The focus is on constrained linear systems and constrained linear hybrid systems. The applicability of the theory is demonstrated through two experimental case studies: a mechanical laboratory process and a traction control system developed jointly with the Ford Motor Company in Michigan.
Nonlinear Control Systems 2004
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Author : Frank Allgower
language : en
Publisher: Elsevier
Release Date : 2005-02-02
Nonlinear Control Systems 2004 written by Frank Allgower and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-02-02 with Science categories.
Constrained Optimization Of Linear Systems For Infinite Horizon Problems
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Author : Charles Roger Glassey
language : en
Publisher:
Release Date : 1965
Constrained Optimization Of Linear Systems For Infinite Horizon Problems written by Charles Roger Glassey and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Control theory categories.
Some methods of optimal control theory are extended with a view toward applications to production and inventory control. A linear, discrete time, deterministic system with vector state and decision variables is optimized relative to a quadratic criterion. The optimal control is shown to be piecewise linear in the state vector when the decision is constrained to be nonnegative, and an algorithm is presented for computing optimal controls. The following results are obtained for the infinite horizon unconstrained problem with no discounting of future costs: (1) necessary conditions for convergence of optimal N-period policies. (2) optimal properties of this limit policy. These results are applied to modify the finite horizon algorithm to obtain optimal controls for the infinite horizon constrained problem. Results of some computations are presented. (Author).
Hybrid Systems Computation And Control
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Author : Manfred Morari
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-03-04
Hybrid Systems Computation And Control written by Manfred Morari 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 2005-03-04 with Computers categories.
This book constitutes the refereed proceedings of the 8th International Workshop on Hybrid Systems: Computation and Control, HSCC 2005, held in Zurich, Switzerland in March 2005. The 40 revised full papers presented together with 2 invited papers and the abstract of an invited talk were carefully reviewed and selected from 91 submissions. The papers focus on modeling, analysis, and implementation of dynamic and reactive systems involving both discrete and continuous behaviors. Among the topics addressed are tools for analysis and verification, control and optimization, modeling, engineering applications, and emerging directions in programming language support and implementation.
Hybrid Systems Computation And Control
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Author : Rajeev Alur
language : en
Publisher: Springer
Release Date : 2004-02-24
Hybrid Systems Computation And Control written by Rajeev Alur and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-02-24 with Computers categories.
This volume contains the proceedings of the 7th Workshop on Hybrid Systems: Computation and Control (HSCC 2004) held in Philadelphia, USA, from March 25 to 27, 2004. The annual workshop on hybrid systems attracts researchers from academia and industry interested in modeling, analysis, and implemen- tion of dynamic and reactive systems involving both discrete and continuous behaviors. The previous workshops in the HSCC series were held in Berkeley, USA(1998),Nijmegen,TheNetherlands(1999),Pittsburgh,USA(2000),Rome, Italy (2001), Palo Alto, USA (2002), and Prague, Czech Republic (2003). This year’s HSCC was organized in cooperation with ACM SIGBED (Special Interest Group on Embedded Systems) and was technically co-sponsored by the IEEE Control Systems Society. The program consisted of 4 invited talks and 43 regular papers selected from 117 regular submissions. The program covered topics such as tools for analysis and veri?cation, control and optimization, modeling, and engineering applica- ons, as in past years, and emerging directions in programming language support and implementation. The program also contained one special session focusing on the interplay between biomolecular networks, systems biology, formal methods, andthecontrolofhybridsystems.
Control And Observer Design For Nonlinear Finite And Infinite Dimensional Systems
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Author : Thomas Meurer
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-09-19
Control And Observer Design For Nonlinear Finite And Infinite Dimensional Systems written by Thomas Meurer 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 2005-09-19 with Technology & Engineering categories.
This volume presents a well balanced combination of state-of-the-art theoretical results in the field of nonlinear controller and observer design, combined with industrial applications stemming from mechatronics, electrical, (bio–) chemical engineering, and fluid dynamics. The unique combination of results of finite as well as infinite–dimensional systems makes this book a remarkable contribution addressing postgraduates, researchers, and engineers both at universities and in industry. The contributions to this book were presented at the Symposium on Nonlinear Control and Observer Design: From Theory to Applications (SYNCOD), held September 15–16, 2005, at the University of Stuttgart, Germany. The conference and this book are dedicated to the 65th birthday of Prof. Dr.–Ing. Dr.h.c. Michael Zeitz to honor his life – long research and contributions on the fields of nonlinear control and observer design.