Wave Propagation, Observation and Control in 1-d Flexible Multi-Structures, Vol. 50
This volume presents a detailed study of partial differential equations on planar graphs modeling networked flexible mechanical structures. Special emphasis is laid on the understanding of wave propagation phenomena, through the analysis of the problems of observability and controllability from small regions of the graph or its boundary. Some of these results are extended to the heat, beam and Schrödinger equations on planar graphs. Designed as a self-contained introductory course on control...
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This volume presents a detailed study of partial differential equations on planar graphs modeling networked flexible mechanical structures. Special emphasis is laid on the understanding of wave propagation phenomena, through the analysis of the problems of observability and controllability from small regions of the graph or its boundary. Some of these results are extended to the heat, beam and Schrödinger equations on planar graphs. Designed as a self-contained introductory course on control and observation of networks, the volume contains also some advanced topics and new techniques which may be of interest for researchers in this area. It also includes a list of open problems and topics for future research.
1Introduction12Preliminaries93Some useful tools254The three string network535General trees1036Some observability and controllability results for general networks1497Simultaneous observation and control from an interior region1678Other equations on networks1839Final remarks and open problems197Some consequences of diophantine approximation theorems205
