Reference Work Entry

Encyclopedia of Applied and Computational Mathematics

pp 1076-1080

Date:

Numerics for the Control of Partial Differential Equations

  • Enrique ZuazuaAffiliated withBCAM – Basque Center for Applied MathematicsIkerbasque – Basque Foundation for Science

Introduction

Control theory is now an old subject. It emerged with the Industrial Revolution and has been continuously evolving since. New technological and industrial processes and mechanisms need new control strategies, and this leads to new Mathematics of Control as well. At present control theory is certainly one of the most interdisciplinary areas of research, and it arises vigorously in most modern applications.

Since its origins (see [3, 12]) the field has evolved tremendously, and different tools have been developed to face the main challenges that require to deal with a variety of models: Ordinary Differential Equations/Partial Differential Equations, Linear/Nonlinear, Deterministic/Stochastic, etc.

Practical control problems can be formulated in many different ways, requiring different kinds of answers, related to the different notions of control; the various possible modeling paradigms; and the degree of precision of the result one is looking for optimal control, controllabilit ...

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