This book is concerned with optimal control problems of dynamical systems described by partial differential equations (PDEs). The content covers the theory and numerical algorithms, starting with open-loop control and ending with closed-loop control. It includes Pontryagin’s maximum principle and the Bellman dynamic programming principle based on the notion of viscosity solution. The Bellman dynamic programming method can produce the optimal control in feedback form, making it more appeali...

This book will focus on the differentiation and regulation of subsets of CD4+ T cells. It will also cover other aspects of research on these cells, which has made great advances in recent years, such as subsets’ plasticity and their role in healthy and disease conditions. The book provides researchers and graduate students with a cutting-edge and comprehensive overview of essential research on CD4+ T cells.

This self-contained book gives a detailed treatment of optimal control theory that enables readers to formulate and solve optimal control problems. With a strong emphasis on problem solving, it provides all the necessary mathematical analyses and derivations of important results, including multiplier theorems and Pontryagin's principle. The text presents various examples and basic concepts of optimal control and describes important numerical methods and computational algorithms for solving...

One of the current main challenges in the area of scientific computing is the design and implementation of accurate numerical models for complex physical systems which are described by time dependent coupled systems of nonlinear PDEs. This volume integrates the works of experts in computational mathematics and its applications, with a focus on modern algorithms which are at the heart of accurate modeling: adaptive finite element methods, conservative finite difference methods and finite vo...

This latest addition to the successful Network Biology series presents current methods for determining the entropy of networks, making it the first to cover the recently established Quantitative Graph Theory.An excellent international team of editors and contributors provides an up-to-date outlook for the field, covering a broad range of graph entropy-related concepts and methods. The topics range from analyzing mathematical properties of methods right up to applying them in real-li...

This book focuses on methods that relate, in one form or another, to the “small-gain theorem”. It is aimed at readers who are interested in learning methods for the design of feedback laws for linear and nonlinear multivariable systems in the presence of model uncertainties. With worked examples throughout, it includes both introductory material and more advanced topics.Divided into two parts, the first covers relevant aspects of linear-systems theory, the second, nonlinear theory....

The volume contains a collection of original papers and surveys in various areas of Differential Equations, Control Theory and Optimization written by well-known specialists and is thus useful for PhD students and researchers in applied mathematics.

This book provides an introduction to the use of geometric partial differential equations in image processing and computer vision. This research area brings a number of new concepts into the field, providing a very fundamental and formal approach to image processing. State-of-the-art practical results in a large number of real problems are achieved with the techniques described in this book. Applications covered include image segmentation, shape analysis, image enhancement, and tracking. T...

This volume features an extensive account of both research and expository papers in a wide area of engineering and mathematics and its various applications.Topics treated within this book include optimization of control points, game theory, equilibrium points, algorithms, Cartan matrices, integral inequalities, Volterra integro-differential equations, Caristi-Kirk theorems, Laplace type integral operators, etc.This useful reference text benefits graduate students, beginning...

This book gathers together a selection of papers presented at the Joint CTS-HYCON Workshop on Nonlinear and Hybrid Control held at the Paris Sorbonne, France, 10-12 July 2006. The main objective of the Workshop was to promote the exchange of ideas and experiences and reinforce scientific contacts in the large multidisciplinary area of the control of nonlinear and hybrid systems.

This book is based on the outcome of the “2012 Interdisciplinary Symposium on Complex Systems” held at the island of Kos. The book consists of 12 selected papers of the symposium starting with a comprehensive overview and classification of complexity problems, continuing by chapters about complexity, its observation, modeling and its applications to solving various problems including real-life applications. More exactly, readers will have an encounter with the structural complexity of vort...

This book focuses on how to implement optimal control problems via the variational method. It studies how to implement the extrema of functional by applying the variational method and covers the extrema of functional with different boundary conditions, involving multiple functions and with certain constraints etc. It gives the necessary and sufficient condition for the (continuous-time) optimal control solution via the variational method, solves the optimal control problems with different ...