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142
Proper orthogonal decomposition (POD) is a
powerful technique for model reduction of non-linear systems. It
is based on a Galerkin type discretization with basis elements
created from the dynamical system itself. In the context of
optimal control this approach may suffer from the fact that the
basis elements are computed from a reference trajectory containing
features which are quite different from those of the optimally
controlled trajectory. A method is proposed which avoids this
problem of unmodelled...
For a riemannian structure on a semidirect product of Lie groups, the variational problems can be reduced using the group symmetry. Choosing the Levi-Civita connection of a positive definite metric tensor, instead of any of the canonical connections for the Lie group, simplifies the reduction of the variations but complicates the expression for the Lie algebra valued covariant derivatives. The origin of the discrepancy is in the semidirect product structure, which implies that the riemannian exponential...
For a Riemannian structure on a
semidirect product of Lie groups, the variational problems can be
reduced using the group symmetry.
Choosing the Levi-Civita connection of a positive definite
metric tensor,
instead of any of the canonical connections for the Lie group,
simplifies the reduction of the variations but complicates the
expression for the Lie algebra valued covariant derivatives.
The origin of the discrepancy is in the semidirect product
structure, which implies that the Riemannian
exponential...
2000 Mathematics Subject Classification: 49J15, 49J30, 53B50.In the context of sub-Riemannian geometry and the Lipschitzian regularity of minimizers in control theory, we investigate some properties of minimizing geodesics for certain affine distributions. In particular, we consider the case of a generalized H2-strong affine distribution and the case of an affine Plaff system of maximal class.
We consider an optimal control problem describing a laser-induced population transfer on a -level quantum system. For a convex cost depending only on the moduli of controls (i.e. the lasers intensities), we prove that there always exists a minimizer in resonance. This permits to justify some strategies used in experimental physics. It is also quite important because it permits to reduce remarkably the complexity of the problem (and extend some of our previous results for and ): instead of looking...
We consider an optimal control problem describing a
laser-induced
population transfer on a n-level quantum system. For a convex cost depending only on the moduli
of controls (i.e. the lasers intensities),
we prove that there always exists a minimizer in
resonance. This permits to justify
some strategies used in experimental physics. It is also quite
important
because it permits to reduce remarkably
the complexity of the problem (and extend some of our previous
results
for n=2 and n=3): instead...
A numerical technique for solving the classical brachistochrone problem in the calculus of variations is presented. The brachistochrone problem is first formulated as a nonlinear optimal control problem. Application of this method results in the transformation of differential and integral expressions into some algebraic equations to which Newton-type methods can be applied. The method is general, and yields accurate results.
We consider a quadratic control problem with a semilinear state equation depending on a small parameter . We show that the optimal control is a regular function of such parameter.
In this work we study the structure of approximate solutions of autonomous variational problems with a lower semicontinuous strictly convex integrand :
In this work we study the structure of approximate
solutions of autonomous variational problems with a lower
semicontinuous strictly convex integrand f : Rn×RnR1, where Rn is the n-dimensional Euclidean
space. We obtain a full...
We analyze the problem of switching controls for control systems endowed with different actuators. The goal is to control the dynamics of the system by switching from an actuator to the other in a systematic way so that, in each instant of time, only one actuator is active. We first address a finite-dimensional model and show that, under suitable rank conditions, switching control strategies exist and can be built in a systematic way. To do this we introduce a new variational principle building...
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