9 edition of **Differential inclusions** found in the catalog.

- 239 Want to read
- 3 Currently reading

Published
**1984** by Springer-Verlag in Berlin, New York .

Written in English

- Differential inclusions.,
- Set-valued maps.,
- Feedback control systems.

**Edition Notes**

Other titles | Viability theory. |

Statement | Jean-Pierre Aubin, Arrigo Cellina. |

Series | Grundlehren der mathematischen Wissenschaften ;, 264 |

Contributions | Cellina, Arrigo, 1941- |

Classifications | |
---|---|

LC Classifications | QA371 .A93 1984 |

The Physical Object | |

Pagination | xiii, 342 p. : |

Number of Pages | 342 |

ID Numbers | |

Open Library | OL2839520M |

ISBN 10 | 0387131051 |

LC Control Number | 84001327 |

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During the 60's and 70's, a special class of differential inclusions was thoroughly investigated: those of the form X'(t)E - A(x(t)), x (0) =xo where A is a "maximal monotone" map.

This class of inclusions contains the class of "gradient inclusions" which generalize the usual gradient equations x'(t) = -VV(x(t)), x(O)=xo when V is a Cited by: This text provides an introductory treatment to the theory of differential inclusions.

Differential inclusions book The reader is only required to know ordinary differential equations, theory of functions, and functional analysis on the elementary level.

Chapter 1 contains a brief introduction to convex analysis. Chapter 2 considers set-valued maps. Search within book. Front Matter. Pages I-XIII. PDF. Introduction.

Jean-Pierre Aubin, Arrigo Cellina. Pages Background Notes. Existence of Solutions to Differential Inclusions. Jean-Pierre Aubin, Arrigo Cellina.

Pages Differential Inclusions with Maximal Monotone Maps. Jean-Pierre Aubin, Arrigo Cellina. Pages Viability. Differential Inclusions Set-Valued Maps and Viability Theory.

Authors: Aubin, J.-P., Cellina, A. Free Preview. The present book is devoted to the investigation of the properties of functional-differential inclusions of the form [x dot](t) [is an element of] F(t,[x subscript t],[x dot subscript t]).

Besides the existence theorems, the book is concerned with basic problems of optimal control theory, such as viability, controllability and existence bf Author: Michal Kisielewicz.

A great impetus to study differential inclusions came from the development of Control Theory, i.e. of dynamical systems x'(t) = f(t, x(t), u(t)), x(O)=xo "controlled" by parameters u(t) (the "controls").

Indeed, if we introduce the set-valued map F(t, x)= {f(t, x, u)}ueu then solutions to the differential equations (*) are solutions to the "differen tial inclusion" (**).

differential inclusions. However, the book is not addressed to mathematicians. The topic could be classified as applied mathematics, but it is rather on modeling and simulation. The aim of the book is to show some properties and applications of differential inclusions, not very popular among the people who work in the field of.

During the last 10 years, the authors have been responsible for extensive contributions to the literature on impulsive differential inclusions via fixed point methods.

This book is motivated by that research as the authors endeavor to bring under one cover much of those results along with results by other researchers either affecting or. This book presents basic concepts and principles of mathematical programming in terms of set-valued analysis and develops a comprehensive optimality theory of problems described by ordinary and partial differential inclusions.

Yong Zhou, in Fractional Evolution Equations and Inclusions, Notes and Remarks. Fractional evolution inclusion is a kind of important differential inclusions describing the processes behaving in a much more complex way on time, which appear as a generalization of fractional evolution Differential inclusions book (such as time-fractional diffusion equations) through the application of.

Huang J, Yu L and Xia S () Stabilization and Finite Time Stabilization of Nonlinear Differential Inclusions Based on Control Lyapunov Function, Circuits, Systems, and Signal Processing,(), Online publication date: 1-Jul The contents of the present book are divided into five Chapters and an Appendix.

The first Chapter of the J>ook has been left without changes and deals with multi-valued differential equations generated by a differential inclusion.

The second Chapter has. COVID Resources. Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle.

Fuzzy differential functions are applicable to real-world problems in engineering, computer science, and social science. That relevance makes for rapid development of new ideas and theories. This volume is a timely introduction to the subject that describes the current state of the theory of fuzzy differential equations and inclusions and.

Summary. Topological Methods for Differential Equations and Inclusions covers the important topics involving topological methods in the theory of systems of differential equations. The equivalence between a control system and the corresponding differential inclusion is the central idea used to prove existence theorems in optimal control theory.

Book Description. Topological Methods for Differential Equations and Inclusions covers the important topics involving topological methods in the theory of systems of differential equations. The equivalence between a control system and the corresponding differential inclusion is the central idea used to prove existence theorems in optimal control theory.

Measurable Selections.- 2. Existence of Solutions to Differential Inclusions.- 1. Convex Valued Differential Inclusions.- 2. Qualitative Properties of the Set of Trajectories of Convex-Valued Differential Inclusions.- 3. Nonconvex-Valued Differential Inclusions.- 4.

Differential Inclusions with Lipschitzean Maps and the Relaxation Theorem.- 5. For continuous differential inclusions the classical bang-bang property is known to fail, yet a weak form of it is established here, in the case where the right hand side is a multifunction whose.

Impulsive Differential Inclusions | Differential equations with impulses arise as models of many evolving processes that are subject to abrupt changes, such as shocks, harvesting, and natural disasters. These phenomena involve short-term perturbations from continuous and smooth dynamics, whose duration is negligible in comparison with the duration of an entire evolution.

The main objective of this survey is to study convergence properties of difference methods applied to differential inclusions. It presents, in a unified way, a Cited by: Purchase Approximation and Optimization of Discrete and Differential Inclusions - 1st Edition. Print Book & E-Book. ISBN Written by an award-winning author in the field of stochastic differential inclusions and their application to control theory, This book is intended for students and researchers in mathematics and applications; particularly those studying optimal control : Springer New York.

For a review of the publications on differential inclusions and on the connection of such inclusions with control problems see. For the concept of stability of differential inclusions see [8], [1] ; for the existence of bounded and periodic solutions, and for other properties, see [1], [6], [7].

We give a reformulation of the Euler equations as a differential inclusion, and in this way we obtain transparent proofs of several celebrated results of V. Scheffer and A. Shnirelman concerning the non-uniqueness of weak solutions and the existence of Cited by: Differential inclusions established as a part of the general theory of differential equations and penetrated different areas of sciences as a consequence of their numerous applications [8][9][ The difference between the family of differential equations and differential inclusion is essentially in the way of studying.

But sometimes there may be slight differences between solutions in some cases. Differential inclusions, for example, are useful in elucidating the properties of. Read "Approximation and Optimization of Discrete and Differential Inclusions" by Elimhan N Mahmudov available from Rakuten Kobo.

Optimal control theory has numerous applications in both science and engineering. This book presents basic concepts and Brand: Elsevier Science. In this chapter, we studied a new class of problems in the theory of optimal control defined by polynomial linear differential operators.

As a result, an interesting Mayer problem arises with higher order differential inclusions. Thus, in terms of the Euler-Lagrange and Hamiltonian type inclusions, sufficient optimality conditions are : Elimhan N.

Mahmudov. where F is a set-valued function on R n × R +.Any x: R + → R n that satisfies () is called a solution or trajectory of the DI ().

Of course, there can be many solutions of the DI (). Our goal is to establish that various properties are satisfied by all solutions of a given DI. Theory of Fuzzy Differential Equations and Inclusions book. By V. Lakshmikantham, Ram N an investigation of the basic theory of fuzzy differential equations, and an introduction to fuzzy differential inclusions.

This volume is a timely introduction to the subject that describes the current state of the theory of fuzzy differential Cited by: Reports and expands upon topics discussed at the International Conference on [title] held in Colorado Springs, Colo., June Presents recent advances in control, oscillation, and stability theories, spanning a variety of subfields and covering 5/5(1).

The book deals with the theory of semilinear differential inclusions in infinite dimensional spaces. In this setting, problems of interest to applications do not suppose neither convexity of the map or compactness of the multi-operators.

Differential Inclusions by Jean-Pierre Aubin,available at Book Depository with free delivery worldwide.5/5(1). used textbook “Elementary differential equations and boundary value problems” by Boyce & DiPrima (John Wiley & Sons, Inc., Seventh Edition, c ).

Many of the examples presented in these notes may be found in this book. The material of Chapter 7 is adapted from the textbook “Nonlinear dynamics and chaos” by Steven. DIFFERENTIAL INCLUSIONS Decomp osable sets in functional spaces T o ev ery di eren tial equation x f t x where is a contin uous mapping de ned on an op en connected subset G of I R n assuming v alues inclusions x F t x let us assume that F is de ned o v er the Cartesian pro duct r D r and tak es compact v alues in D for some r and W e also.

Destination page number Search scope Search Text Search scope Search Text. Differential Inclusions in Modeling and Simulation: Interdisciplinary Applications, Reachable Sets, Uncertainty Treatment for Educators and Researcher, ISBNISBNBrand New, Free shipping in the US.

Differential inclusions (DIs) are used as an generalization of the ODE models. An important topic of the book that appears in nearly all examples is the.

Fractional evolution inclusions are an important form of differential inclusions within nonlinear mathematical analysis. They are generalizations of the much more widely developed fractional evolution equations (such as time-fractional diffusion equations) seen through the lens of multivariate analysis.

In mathematics, a differential variational inequality (DVI) is a dynamical system that incorporates ordinary differential equations and variational inequalities or complementarity problems. DVIs are useful for representing models involving both dynamics and inequality constraints.

Examples of such problems include, for example, mechanical impact problems, electrical circuits with ideal. This Special Issue invites papers that focus on recent and novel developments in the theory of any types of differential and fractional differential equations and inclusions, especially on analytical and numerical results for fractional ordinary and partial differential equations.This book deals with the existence and stability of solutions to initial and boundary value problems for functional differential and integral equations and inclusions involving the Riemann-Liouville, Caputo, and Hadamard fractional derivatives and integrals.

A wide variety of topics is covered in a mathematically rigorous manner making this work a valuable source of .Stanford Libraries' official online search tool for books, media, journals, databases, government documents and more.