Giuseppe Buttazzo
Dipartimento di Matematica, Universita di Pisa, Via Buonarroti, 2,
56127 PISA (Italy)
Optimization Problems with Manifolds as Controls
We present an attempt to treat optimal control problems where
the control variable is a manifold. The problems are written in the form
\min {F(M,u) : M \in{\cal M}, u\in X(M), E_M(u)=0}
where the manifold M plays the role of control variable, {\cal M} is the
class of admissible choices, X(M) is the space of states, F is the cost
functional, and E_M is some differential operator on M which provides the
state equation. A typical example of this kind of problems is given by the
Euler elastica. The idea is to relax the problem embedding the class of
admissible controls into the larger class of nonnegative measures.
Abstract in Postscript
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