Optimal Control Problems for Partial Differential Equations on Reticulated Domains

This book offers a method based on asymptotic analysis aimed at combining techniques of homogenization and approximation to cover optimal control problems defined on reticulated domains, networked systems such as lattice, honeycomb, or hierarchical structures.

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Optimal control of partial differential equations (PDEs) is a well-established discipline in mathematics with many interfaces to science and engineering. During the development of this area, the complexity of the systems to be controlled has also increased significantly; however, the numerical realization of these complex systems has become an issue in scientific computing, as the number of variables involved may easily exceed a couple of million.

In order to carry out model-reduction on these systems, the authors of this work have developed a method based on asymptotic analysis. They aim at combining techniques of homogenization and approximation in order to cover optimal control problems defined on reticulated domains, networked systems such as lattice, honeycomb, or hierarchical structures. Because of these structures' complicated geometry, the asymptotic analysis is even more important, as a direct numerical computation of solutions would be extremely difficult. The work's first part can be used as an advanced textbook on abstract optimal control problems, in particular on reticulated domains, while the second part serves as a research monograph where stratified applications are discussed.

Optimal Control Problems for Partial Differential Equations on Reticulated Domains is an excellent reference for graduate students, researchers, and practitioners in mathematics and areas of engineering involving reticulated domains and networked systems.