Time Dependent Subdifferential Evolution Inclusions and Optimal ControlTime Dependent Subdifferential Evolution Inclusions and Optimal Control



[103] G. Stassinopoulos and R. Vinter, CONTINUOUS DEPENDENCE OF soluTIONS of A DIFFERENTIAL INCLUSION ON THE RIGHT HAND SIDE WITH APPLICATIONS TO STABILITY OF OPTIMAL CoNTROL PROBLEMs, SIAM J. Control Optim., 17 (1979), 432–449.

Author: Shouchuan Hu

Publisher: American Mathematical Soc.

ISBN: 9780821807798

Category:

Page: 81

View: 203

This volume studies multivalued evolution equations driven by time-dependent subdifferential operators and optimal control problems for such systems. The formulation is general enough to incorporate problems with time varying constraints. For evolution inclusions, existence relaxation and structural results for the solution set are proved. For optimal control problems, a general existence theory is developed, different forms of the relaxed problem are introduced and studied, well-posedness properties are investigated and the precise relation between the properties of relaxability and well-posedness is established. Various examples of systems which fit in the abstract framework are analyzed.

Stochastic Differential Inclusions and ApplicationsStochastic Differential Inclusions and Applications



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 ...

Author: Michał Kisielewicz

Publisher: Springer Science & Business Media

ISBN: 9781461467564

Category:

Page: 282

View: 547

​This book aims to further develop the theory of stochastic functional inclusions and their applications for describing the solutions of the initial and boundary value problems for partial differential inclusions. The self-contained volume is designed to introduce the reader in a systematic fashion, to new methods of the stochastic optimal control theory from the very beginning. The exposition contains detailed proofs and uses new and original methods to characterize the properties of stochastic functional inclusions that, up to the present time, have only been published recently by the author. The work is divided into seven chapters, with the first two acting as an introduction, containing selected material dealing with point- and set-valued stochastic processes, and the final two devoted to applications and optimal control problems. The book presents recent and pressing issues in stochastic processes, control, differential games, optimization and their application in finance, manufacturing, queueing networks, and climate control. 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 theory. It is also highly relevant for students of economics and engineering. The book can also be used as a reference on stochastic differential inclusions. Knowledge of select topics in analysis and probability theory are required.

Introduction to the Theory of Differential InclusionsIntroduction to the Theory of Differential Inclusions



[107] G.V. Smirnov, Discrete approximations and optimal solutions to differential inclusions, Cybernetics, 27 (1991), 101-107. ... [111] G.V. Smirnov, Stabilization by constrained controls, SIAM J. Control Opt., 34 (1996), 1616-1649.

Author: Georgi V. Smirnov

Publisher: American Mathematical Soc.

ISBN: 9780821829776

Category:

Page: 226

View: 451

Differential inclusions play an important role as a tool in the study of various dynamical processes described by equations with a discontinuous or multivalued right-hand side. This text acts as an introduction to the subject.

Advances in Mathematical Modeling Optimization and Optimal ControlAdvances in Mathematical Modeling Optimization and Optimal Control



This book contains extended, in-depth presentations of the plenary talks from the 16th French-German-Polish Conference on Optimization, held in Kraków, Poland in 2013.

Author: Jean-Baptiste Hiriart-Urruty

Publisher: Springer

ISBN: 9783319307855

Category:

Page: 201

View: 870

This book contains extended, in-depth presentations of the plenary talks from the 16th French-German-Polish Conference on Optimization, held in Kraków, Poland in 2013. Each chapter in this book exhibits a comprehensive look at new theoretical and/or application-oriented results in mathematical modeling, optimization, and optimal control. Students and researchers involved in image processing, partial differential inclusions, shape optimization, or optimal control theory and its applications to medical and rehabilitation technology, will find this book valuable. The first chapter by Martin Burger provides an overview of recent developments related to Bregman distances, which is an important tool in inverse problems and image processing. The chapter by Piotr Kalita studies the operator version of a first order in time partial differential inclusion and its time discretization. In the chapter by Günter Leugering, Jan Sokołowski and Antoni Żochowski, nonsmooth shape optimization problems for variational inequalities are considered. The next chapter, by Katja Mombaur is devoted to applications of optimal control and inverse optimal control in the field of medical and rehabilitation technology, in particular in human movement analysis, therapy and improvement by means of medical devices. The final chapter, by Nikolai Osmolovskii and Helmut Maurer provides a survey on no-gap second order optimality conditions in the calculus of variations and optimal control, and a discussion of their further development.

Optimal Control Stabilization and Nonsmooth AnalysisOptimal Control Stabilization and Nonsmooth Analysis



Kisielewicz M ( 1991 ) Differential Inclusions and Optimal Control . Kluwer Dordrecht The Netherlands 4. Mordukhovich B ( 1976 ) Maximum principle in problems of time optimal control with nonsmooth constraints , J Appl Math Mech 40 ...

Author: Marcio S. de Queiroz

Publisher: Springer Science & Business Media

ISBN: 3540213309

Category:

Page: 361

View: 149

This edited book contains selected papers presented at the Louisiana Conference on Mathematical Control Theory (MCT'03), which brought together over 35 prominent world experts in mathematical control theory and its applications. The book forms a well-integrated exploration of those areas of mathematical control theory in which nonsmooth analysis is having a major impact. These include necessary and sufficient conditions in optimal control, Lyapunov characterizations of stability, input-to-state stability, the construction of feedback mechanisms, viscosity solutions of Hamilton-Jacobi equations, invariance, approximation theory, impulsive systems, computational issues for nonlinear systems, and other topics of interest to mathematicians and control engineers. The book has a strong interdisciplinary component and was designed to facilitate the interaction between leading mathematical experts in nonsmooth analysis and engineers who are increasingly using nonsmooth analytic tools.