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Dynamical shape control and the stabilization of non‐linear thin rods
Author(s) -
Sokolowski J.,
Sprekels J.
Publication year - 1991
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670140104
Subject(s) - mathematics , monotone polygon , rod , domain (mathematical analysis) , hysteresis , mathematical analysis , control theory (sociology) , control (management) , geometry , physics , computer science , medicine , alternative medicine , pathology , artificial intelligence , quantum mechanics
In this paper we consider the problem of stabilizing the motion of the tip of a thin rod by controlling the shape of the rod, that is its length, dynamically. Well‐posedness of the associated state equations, valid on a moving domain, is proved, and the necessary conditions of optimality for the control problem are derived. The theory applies to materials where the stress–strain relation is both non‐linear and non monotone, so that hysteresis effects arising from solid–solid phase transitions in the rod are included.