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Author: Prabhjeet Singh Arora
Publisher:
ISBN:
Category :
Languages : en
Pages : 101
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Book Description
Determination of the set of all possible states, which a system can attain, plays an important role in safety for critical application. Prior knowledge of this set for the complete run-time provides critical information about how a system may evolve, providing accurate information of all the states, which could violate constraints. The knowledge of these states, helps in estimating control input, which can control the system, such that, these states are eliminated from the reachable set. Computation of reachable set of a dynamic system for a set of initial conditions can be easily performed, provided the analytical solution of the system for all initial conditions can be obtained. However, obtaining analytical solutions for nonlinear systems is a non-trivial task. Therefore, numerical methods are constructed, to obtain approximate solutions for these systems. Owing to the recent advancements in computational technology, it is now possible to tackle nonlinear systems using numerical methods. The reduction in computation al errors and the increase in the rate of computation have enhanced the quality of results obtained from discrete approximations of continuous systems. The iterative property of these discrete approximations can be implemented in the form of algorithms. These algorithms, in turn, compute precise numerical solutions of systems for which analytical solutions are otherwise difficult to obtain. The primary objective of this thesis is to formulate and construct algorithms to compute reachable sets for linear systems and extending these algorithms to compute reachable sets for linear systems with perturbations. The secondary objective is to apply and verify the algorithms on a real-world application, previously studied in the open literature, and to discuss the results obtained. The computation of a reachable set is carried out in MATLAB® and the computed reachable sets for representative mathematical models of dynamic systems are presented and different ideas of reachable states are discussed.
Author: Prabhjeet Singh Arora
Publisher:
ISBN:
Category :
Languages : en
Pages : 101
Get Book Here
Book Description
Determination of the set of all possible states, which a system can attain, plays an important role in safety for critical application. Prior knowledge of this set for the complete run-time provides critical information about how a system may evolve, providing accurate information of all the states, which could violate constraints. The knowledge of these states, helps in estimating control input, which can control the system, such that, these states are eliminated from the reachable set. Computation of reachable set of a dynamic system for a set of initial conditions can be easily performed, provided the analytical solution of the system for all initial conditions can be obtained. However, obtaining analytical solutions for nonlinear systems is a non-trivial task. Therefore, numerical methods are constructed, to obtain approximate solutions for these systems. Owing to the recent advancements in computational technology, it is now possible to tackle nonlinear systems using numerical methods. The reduction in computation al errors and the increase in the rate of computation have enhanced the quality of results obtained from discrete approximations of continuous systems. The iterative property of these discrete approximations can be implemented in the form of algorithms. These algorithms, in turn, compute precise numerical solutions of systems for which analytical solutions are otherwise difficult to obtain. The primary objective of this thesis is to formulate and construct algorithms to compute reachable sets for linear systems and extending these algorithms to compute reachable sets for linear systems with perturbations. The secondary objective is to apply and verify the algorithms on a real-world application, previously studied in the open literature, and to discuss the results obtained. The computation of a reachable set is carried out in MATLAB® and the computed reachable sets for representative mathematical models of dynamic systems are presented and different ideas of reachable states are discussed.
Author: M. Pachter
Publisher:
ISBN: 9780798810401
Category :
Languages : en
Pages : 6
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Book Description
Author: Pierre-Jean Meyer
Publisher: Springer Nature
ISBN: 303065110X
Category : Technology & Engineering
Languages : en
Pages : 115
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Book Description
This brief presents a suite of computationally efficient methods for bounding trajectories of dynamical systems with multi-dimensional intervals, or ‘boxes’. It explains the importance of bounding trajectories for evaluating the robustness of systems in the face of parametric uncertainty, and for verification or control synthesis problems with respect to safety and reachability properties. The methods presented make use of: interval analysis; monotonicity theory; contraction theory; and data-driven techniques that sample trajectories. The methods are implemented in an accompanying open-source Toolbox for Interval Reachability Analysis. This brief provides a tutorial description of each method, focusing on the requirements and trade-offs relevant to the user, requiring only basic background on dynamical systems. The second part of the brief describes applications of interval reachability analysis. This makes the brief of interest to a wide range of academic researchers, graduate students, and practising engineers in the field of control and verification.
Author: Paul Alexandroff
Publisher: Courier Corporation
ISBN: 0486155064
Category : Mathematics
Languages : en
Pages : 68
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Book Description
Concise work presents topological concepts in clear, elementary fashion, from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups. Includes 25 figures.
Author: Dmitry Balandin
Publisher: Springer Nature
ISBN: 3030787591
Category : Computers
Languages : en
Pages : 418
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Book Description
This book constitutes selected and revised papers from the 20th International Conference on Mathematical Modeling and Supercomputer Technologies, MMST 2020, held in Nizhny Novgorod, Russia, in November 2020. Due to the COVID-19 pandemic the conference was held online. The 25 full papers and 8 short papers presented in the volume were thoroughly reviewed and selected from the 106 submissions. They are organized in topical secions on computational methods for mathematical models analysis; computation in optimization and optimal control; supercomputer simulation.
Author: Joao Hespanha
Publisher: Springer Science & Business Media
ISBN: 3540331700
Category : Computers
Languages : en
Pages : 595
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Book Description
This book constitutes the refereed proceedings of the 9th International Workshop on Hybrid Systems: Computation and Control, HSCC 2006, held in Santa Barbara, CA, USA in March 2006. The 39 revised full papers presented together with the abstracts of 3 invited talks were carefully reviewed and selected from 79 submissions. 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. The papers focus on modeling, analysis, and implementation of dynamic and reactive systems involving both discrete and continuous behaviors.
Author: George Fisher List
Publisher:
ISBN:
Category : Set theory
Languages : en
Pages : 60
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Book Description
Author: João P. Hespanha
Publisher: Princeton University Press
ISBN: 0691179573
Category : Mathematics
Languages : en
Pages : 352
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Book Description
A fully updated textbook on linear systems theory Linear systems theory is the cornerstone of control theory and a well-established discipline that focuses on linear differential equations from the perspective of control and estimation. This updated second edition of Linear Systems Theory covers the subject's key topics in a unique lecture-style format, making the book easy to use for instructors and students. João Hespanha looks at system representation, stability, controllability and state feedback, observability and state estimation, and realization theory. He provides the background for advanced modern control design techniques and feedback linearization and examines advanced foundational topics, such as multivariable poles and zeros and LQG/LQR. The textbook presents only the most essential mathematical derivations and places comments, discussion, and terminology in sidebars so that readers can follow the core material easily and without distraction. Annotated proofs with sidebars explain the techniques of proof construction, including contradiction, contraposition, cycles of implications to prove equivalence, and the difference between necessity and sufficiency. Annotated theoretical developments also use sidebars to discuss relevant commands available in MATLAB, allowing students to understand these tools. This second edition contains a large number of new practice exercises with solutions. Based on typical problems, these exercises guide students to succinct and precise answers, helping to clarify issues and consolidate knowledge. The book's balanced chapters can each be covered in approximately two hours of lecture time, simplifying course planning and student review. Easy-to-use textbook in unique lecture-style format Sidebars explain topics in further detail Annotated proofs and discussions of MATLAB commands Balanced chapters can each be taught in two hours of course lecture New practice exercises with solutions included
Author: Paul A. Fuhrmann
Publisher: Springer
ISBN: 3319166468
Category : Mathematics
Languages : en
Pages : 670
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Book Description
This book provides the mathematical foundations of networks of linear control systems, developed from an algebraic systems theory perspective. This includes a thorough treatment of questions of controllability, observability, realization theory, as well as feedback control and observer theory. The potential of networks for linear systems in controlling large-scale networks of interconnected dynamical systems could provide insight into a diversity of scientific and technological disciplines. The scope of the book is quite extensive, ranging from introductory material to advanced topics of current research, making it a suitable reference for graduate students and researchers in the field of networks of linear systems. Part I can be used as the basis for a first course in Algebraic System Theory, while Part II serves for a second, advanced, course on linear systems. Finally, Part III, which is largely independent of the previous parts, is ideally suited for advanced research seminars aimed at preparing graduate students for independent research. “Mathematics of Networks of Linear Systems” contains a large number of exercises and examples throughout the text making it suitable for graduate courses in the area.
Author: Peter Butkovič
Publisher: Springer Science & Business Media
ISBN: 1849962995
Category : Mathematics
Languages : en
Pages : 281
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Book Description
Recent years have seen a significant rise of interest in max-linear theory and techniques. Specialised international conferences and seminars or special sessions devoted to max-algebra have been organised. This book aims to provide a first detailed and self-contained account of linear-algebraic aspects of max-algebra for general (that is both irreducible and reducible) matrices. Among the main features of the book is the presentation of the fundamental max-algebraic theory (Chapters 1-4), often scattered in research articles, reports and theses, in one place in a comprehensive and unified form. This presentation is made with all proofs and in full generality (that is for both irreducible and reducible matrices). Another feature is the presence of advanced material (Chapters 5-10), most of which has not appeared in a book before and in many cases has not been published at all. Intended for a wide-ranging readership, this book will be useful for anyone with basic mathematical knowledge (including undergraduate students) who wish to learn fundamental max-algebraic ideas and techniques. It will also be useful for researchers working in tropical geometry or idempotent analysis.
