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Author: Frank Christophersen
Publisher: Springer
ISBN: 3540727019
Category : Technology & Engineering
Languages : en
Pages : 196
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Book Description
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.
Author: Frank Christophersen
Publisher: Springer
ISBN: 3540727019
Category : Technology & Engineering
Languages : en
Pages : 196
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Book Description
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.
Author: Frank J. Christophersen
Publisher:
ISBN:
Category :
Languages : en
Pages : 190
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Book Description
Author: Thomas Besselmann
Publisher: CreateSpace
ISBN: 9781453842515
Category : Technology & Engineering
Languages : en
Pages : 294
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Book Description
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.
Author: Luis Rodrigues
Publisher: SIAM
ISBN: 1611975905
Category : Mathematics
Languages : en
Pages : 224
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Book Description
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.
Author: Francesco Borrelli
Publisher: Springer
ISBN: 3540362258
Category : Mathematics
Languages : en
Pages : 206
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Book Description
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.
Author: Daniel Görges
Publisher: Logos Verlag Berlin GmbH
ISBN: 3832530967
Category : Computers
Languages : en
Pages : 204
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Book Description
This thesis addresses optimal control of discrete-time switched linear systems with application to networked embedded control systems (NECSs). Part I focuses on optimal control and scheduling of discrete-time switched linear systems. The objective is to simultaneously design a control law and a switching (scheduling) law such that a cost function is minimized. This optimization problem exhibits exponential complexity. Taming the complexity is a major challenge. Two novel methods are presented to approach this optimization problem: Receding-horizon control and scheduling relies on the receding horizon principle. The optimization problem is solved based on relaxed dynamic programming, allowing to reduce complexity by relaxing optimality within predefined bounds. The solution can be expressed as a piecewise linear (PWL) state feedback control law. Stability is addressed via an a priori stability condition based on a terminal weighting matrix and several a posteriori stability criteria based on constructing piecewise quadratic Lyapunov functions and on utilizing the cost function as a candidate Lyapunov function. Moreover, a region-reachability criterion is derived. Periodic control and scheduling relies on periodic control theory. Both offline and online scheduling are studied. The optimization problem is solved based on periodic control and exhaustive search. The online scheduling solution can again be expressed as a PWL state feedback control law. Stability is guaranteed inherently. Several methods are proposed to reduce the online complexity based on relaxation and heuristics. Part II focuses on optimal control and scheduling of NECSs. The NECS is modeled as a block-diagonal discrete-time switched linear system. Various control and scheduling codesign strategies are derived based on the methods from Part I regarding the structural properties of NECSs. The methods presented in Part I and II are finally evaluated in a case study.
Author: Rolf Findeisen
Publisher: Springer
ISBN: 3540726993
Category : Technology & Engineering
Languages : en
Pages : 644
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Book Description
Thepastthree decadeshaveseenrapiddevelopmentin the areaofmodelpred- tive control with respect to both theoretical and application aspects. Over these 30 years, model predictive control for linear systems has been widely applied, especially in the area of process control. However, today’s applications often require driving the process over a wide region and close to the boundaries of - erability, while satisfying constraints and achieving near-optimal performance. Consequently, the application of linear control methods does not always lead to satisfactory performance, and here nonlinear methods must be employed. This is one of the reasons why nonlinear model predictive control (NMPC) has - joyed signi?cant attention over the past years,with a number of recent advances on both the theoretical and application frontier. Additionally, the widespread availability and steadily increasing power of today’s computers, as well as the development of specially tailored numerical solution methods for NMPC, bring thepracticalapplicabilityofNMPCwithinreachevenforveryfastsystems.This has led to a series of new, exciting developments, along with new challenges in the area of NMPC.
Author: Rajeev Alur
Publisher: Springer Science & Business Media
ISBN: 3540212590
Category : Computers
Languages : en
Pages : 686
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Book Description
This book constitutes the refereed proceedings of the 7th International Workshop on Hybrid Systems: Computation and Control, HSCC 2004, held in Philadelphia, PA, USA, in March 2004. The 43 revised full papers presented together with an invited article were carefully reviewed and selected from 117 submissions. The papers address all current issues in hybrid systems such as tools for analysis and verification, control and optimization, modeling and engineering applications, and emerging topics in programming language support and implementation; a special focus is on the interplay between biomolecular networks, systems biology, formal methods, and control of hybrid systems.
Author: Matthias Rungger
Publisher: kassel university press GmbH
ISBN: 3862193667
Category : Nonlinear control theory
Languages : en
Pages : 150
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Book Description
Author: Joao Hespanha
Publisher: Springer
ISBN: 3540331719
Category : Computers
Languages : en
Pages : 595
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Book Description
These are the proceedings of the 9th International Workshop on Hybrid Systems: Computation and Control, HSCC 2006, March 2006. 39 revised papers are presented together with the abstracts of 3 invited talks. The focus is on modeling, analysis, and implementation of dynamic and reactive systems involving both discrete and continuous behaviors. Topics addressed include tools for analysis and verification, control and optimization, modeling, engineering applications, and new directions in language support and implementation.
