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- Juan Carlos De los Reyes
- [TMA4183 2017v] Optimization II: Optimal Control of PDEs
- Optimal Control of Partial Differential Equations II: Theory and Applications

Linear and non-linear partial differential equations PDEs constitute one of the most widely used mathematical framework for modelling various physical or technological processes, such as fluid flow, structural deformations, propagation of acoustic and electromagnetic waves among countless other examples. Improvement in such processes therefore require modelling and solving optimization problems constrained with PDEs, and more generally convex and non-convex optimization problems in spaces of functions. In this course you will learn the theory pertinent for analysing optimization problems of this type and also fundamental numerical methods for solving these problems. We will mostly concentrate on the optimal control of processes governed with linear and semilinear elliptic PDEs.

Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. DOI: Optimal control theory is concerned with finding control functions that minimize cost functions for systems described by differential equations. The methods have found widespread applications in aeronautics, mechanical engineering, the life sciences, and many other disciplines.

Optimal control theory is concerned with finding control functions that minimize cost functions for systems described by differential equations. The methods have found widespread applications in aeronautics, mechanical engineering, the life sciences, and many other disciplines. This book focuses on optimal control problems where the state equation is an elliptic or parabolic partial differential equation. Included are topics such as the existence of optimal solutions, necessary optimality conditions and adjoint equations, second-order sufficient conditions, and main principles of selected numerical techniques. It also contains a survey on the Karush-Kuhn-Tucker theory of nonlinear programming in Banach spaces.

Optimal control of partial differential equations and nonlinear optimization Mathematical research topic of WIAS. Research Research Topics. Diese Seite auf Deutsch. Many processes in nature and technology can only be described by partial differential equations, e. Additionally to challenges in modeling, in various applications the manipulation or controlling of the modeled system is also of interest in order to obtain a certain purpose. One ends up in optimal control problems, i. However, in many technical applications additional pointwise constraints to the state or the control are essential, for instance in steel hardening or in optimization of semiconductor crystal growth.

The purpose of this conference is to examine the control theory of partial differential equations and its application. This text is divided into five chapters that primarily focus on tutorial lecture series on the theory of optimal control of distributed systems. It describes the many manifestations of the theory and its applications appearing in the other chapters. This work also presents the principles of the duality and asymptotic methods in control theory, including the variational principle for the heat equation. A chapter highlights systems that are not of the linear quadratic type.

Correspondence should be addressed to Xinguang Zhang; zxg This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This special issue focuses on the theme Complex Boundary Value Problems of Nonlinear Differential Equations: Theory, Computational Methods, and Applications which plays a tremendous role in the study and control of the real-world systems and the development of new technologies. The special issue aim is to present some of the recent developments in this field. The issue contains 36 papers selected through a peer-reviewed process.

*Dedicated to Prof. Eduardo Casas on the occasion of his 60th birthday.*

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## Laurindo A.

The methods have found widespread applications in aeronautics, mechanical Optimal Control of Partial Differential Equations: Theory, Methods and.