Zonotopes

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Zonotopes

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Author : Vu Tuan Hieu Le
language : en
Publisher: John Wiley & Sons
Release Date : 2013-12-04

Zonotopes written by Vu Tuan Hieu Le 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 2013-12-04 with Technology & Engineering categories.

This title focuses on two significant problems in the field of automatic control, in particular state estimation and robust Model Predictive Control under input and state constraints, bounded disturbances and measurement noises. The authors build upon previous results concerning zonotopic set-membership state estimation and output feedback tube-based Model Predictive Control. Various existing zonotopic set-membership estimation methods are investigated and their advantages and drawbacks are discussed, making this book suitable both for researchers working in automatic control and industrial partners interested in applying the proposed techniques to real systems. The authors proceed to focus on a new method based on the minimization of the P-radius of a zonotope, in order to obtain a good trade-off between the complexity and the accuracy of the estimation. They propose a P-radius based set-membership estimation method to compute a zonotope containing the real states of a system, which are consistent with the disturbances and measurement noise. The problem of output feedback control using a zonotopic set-membership estimation is also explored. Among the approaches from existing literature on the subject, the implementation of robust predictive techniques based on tubes of trajectories is developed. Contents 1. Uncertainty Representation Based on Set Theory. 2. Several Approaches on Zonotopic Guaranteed Set-Membership Estimation. 3. Zonotopic Guaranteed State Estimation Based on P-Radius Minimization. 4. Tube Model Predictive Control Based on Zonotopic Set-Membership Estimation. About the Authors Vu Tuan Hieu Le is a Research Engineer at the IRSEEM/ESIGELEC Technopôle du Madrillet, Saint Etienne du Rouvray, France. Cristina Stoica is Assistant Professor in the Automatic Control Department at SUPELEC Systems Sciences (E3S), France. Teodoro Alamo is Professor in the Department of Systems Engineering and Automatic Control at the University of Seville, Spain. Eduardo F. Camacho is Professor in the Department of Systems Engineering and Automatic Control at the University of Seville, Spain. Didier Dumur is Professor in the Automatic Control Department, SUPELEC Systems Sciences (E3S), France.

Extreme Problems For Zonotopes

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Author : Michael Paul Filliman
language : en
Publisher:
Release Date : 1986

Extreme Problems For Zonotopes written by Michael Paul Filliman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with categories.

Tilings Of Zonotopes

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Author : Guy David Bailey
language : en
Publisher:
Release Date : 1997

Tilings Of Zonotopes written by Guy David Bailey and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.

Notes On Lattice Points Of Zonotopes And Lattice Face Polytopes

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Author :
language : en
Publisher:
Release Date : 2010

Notes On Lattice Points Of Zonotopes And Lattice Face Polytopes written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.

Zonotopes Associated With Higher Bruhat Orders

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Author : Stefan Felsner
language : en
Publisher:
Release Date : 1999

Zonotopes Associated With Higher Bruhat Orders written by Stefan Felsner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.

Approximation Of Zonoids By Zonotopes

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Author : J. Bourgain
language : en
Publisher:
Release Date : 1987

Approximation Of Zonoids By Zonotopes written by J. Bourgain and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with categories.

A Calculus Of Complex Zonotopes For Invariance And Stability Verification Of Hybrid Systems

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Author : Santosh Arvind Adimoolam
language : en
Publisher:
Release Date : 2018

A Calculus Of Complex Zonotopes For Invariance And Stability Verification Of Hybrid Systems written by Santosh Arvind Adimoolam 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.

Computing reachable sets is a de facto approach used in many formal verification methods for hybrid systems. But exact computation of the reachable set is an in- tractable problem for many kinds of hybrid systems, either due to undecidability or high computational complexity. Alternatively, quite a lot of research has been focused on using set representations that can be efficiently manipulated to com- pute sufficiently accurate over-approximation of the reachable set. Zonotopes are a useful set representation in reachability analysis because of their closure and low complexity for computing linear transformation and Minkowski sum operations. But for approximating the unbounded time reachable sets by positive invariants, zonotopes have the following drawback. The effectiveness of a set representation for computing a positive invariant depends on efficiently encoding the directions for convergence of the states to an equilibrium. In an affine hybrid system, some of the directions for convergence can be encoded by the complex valued eigen- vectors of the transformation matrices. But the zonotope representation can not exploit the complex eigenstructure of the transformation matrices because it only has real valued generators.Therefore, we extend real zonotopes to the complex valued domain in a way that can capture contraction along complex valued vectors. This yields a new set representation called complex zonotope. Geometrically, complex zonotopes repre- sent a wider class of sets that include some non-polytopic sets as well as polytopic zonotopes. They retain the merit of real zonotopes that we can efficiently perform linear transformation and Minkowski sum operations and compute the support function. Additionally, we show that they can capture contraction along complex valued eigenvectors. Furthermore, we develop computationally tractable approx- imations for inclusion-checking and intersection with half-spaces. Using these set operations on complex zonotopes, we develop convex programs to verify lin- ear invariance properties of discrete time affine hybrid systems and exponential stability of linear impulsive systems. Our experiments on some benchmark exam- ples demonstrate the efficiency of the verification techniques based on complex zonotopes.

A Survey Of Zonotopes

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Author : Joel A. Keranen
language : en
Publisher:
Release Date : 1995

A Survey Of Zonotopes written by Joel A. Keranen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with categories.

Hybrid Systems Computation And Control

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Author : Manfred Morari
language : en
Publisher: Springer
Release Date : 2005-02-25

Hybrid Systems Computation And Control written by Manfred Morari and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-02-25 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.

Computer Aided Verification

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Author : Ahmed Bouajjani
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-06-19

Computer Aided Verification written by Ahmed Bouajjani 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 2009-06-19 with Computers categories.

This book constitutes the refereed proceedings of the 21st International Conference on Computer Aided Verification, CAV 2009, held in Grenoble, France, in June/July 2009. The 36 revised full papers presented together with 16 tool papers and 4 invited talks and 4 invited tutorials were carefully reviewed and selected from 135 regular paper and 34 tool paper submissions. The papers are dedicated to the advancement of the theory and practice of computer-aided formal analysis methods for hardware and software systems; their scope ranges from theoretical results to concrete applications, with an emphasis on practical verification tools and the underlying algorithms and techniques.