2,506 research outputs found
Planar tilting maneuver of a spacecraft: singular arcs in the minimum time problem and chattering
In this paper, we study the minimum time planar tilting maneuver of a
spacecraft, from the theoretical as well as from the numerical point of view,
with a particular focus on the chattering phenomenon. We prove that there exist
optimal chattering arcs when a singular junction occurs. Our study is based on
the Pontryagin Maximum Principle and on results by M.I. Zelikin and V.F.
Borisov. We give sufficient conditions on the initial values under which the
optimal solutions do not contain any singular arc, and are bang-bang with a
finite number of switchings. Moreover, we implement sub-optimal strategies by
replacing the chattering control with a fixed number of piecewise constant
controls. Numerical simulations illustrate our results.Comment: 43 pages, 18 figure
Minimum time control of the rocket attitude reorientation associated with orbit dynamics
In this paper, we investigate the minimal time problem for the guidance of a
rocket, whose motion is described by its attitude kinematics and dynamics but
also by its orbit dynamics. Our approach is based on a refined geometric study
of the extremals coming from the application of the Pontryagin maximum
principle. Our analysis reveals the existence of singular arcs of higher-order
in the optimal synthesis, causing the occurrence of a chattering phenomenon,
i.e., of an infinite number of switchings when trying to connect bang arcs with
a singular arc.
We establish a general result for bi-input control-affine systems, providing
sufficient conditions under which the chattering phenomenon occurs. We show how
this result can be applied to the problem of the guidance of the rocket. Based
on this preliminary theoretical analysis, we implement efficient direct and
indirect numerical methods, combined with numerical continuation, in order to
compute numerically the optimal solutions of the problem.Comment: 33 pages, 14 figure
Extreme rays of the -Schur Cone
We discuss several partial results towards proving Dennis White's conjecture
on the extreme rays of the -Schur cone. We are interested in which
vectors are extreme in the cone generated by all products of Schur functions of
partitions with or fewer parts. For the case where , White
conjectured that the extreme rays are obtained by excluding a certain family of
"bad pairs," and proved a special case of the conjecture using Farkas' Lemma.
We present an alternate proof of the special case, in addition to showing more
infinite families of extreme rays and reducing White's conjecture to two
simpler conjectures.Comment: This paper has been withdrawn by the authors due to a
misinterpretation of the generalized Littlewood-Richardson rule in several
proof
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