2 ms·
I don't know which paper they mean, but here's a relevant paragraph from one of the papers available from Blackmore's page: "In this paper, we unify the convex
by theoh 8y ago
I don't know which paper they mean, but here's a relevant paragraph from one of the papers available from Blackmore's page:
"In this paper, we unify the convex optimization approaches
of [1], [2], [17] and extend them to handle thrust pointing
constraints. While convexifying the problem with nonconvex
thrust pointing constraints, we develop a geometrical insight
into the problem that establishes a connection with “normal
systems” [18]. A normal linear system is defined in the context
of optimal control theory where the system is said to be normal
with respect a set of feasible controls if it maximizes the
Hamiltonian at a unique point of the set of feasible controls. In
the case when the set of feasible controls is convex, a system
being normal implies that the Hamiltonian is maximized at an
extreme point of the set [18]. Our convexification result has
a similar geometric interpretation since it establishes lossless
convexification by ensuring that the Hamiltonian is maximized
at the extreme points of a projection of the relaxed set of
feasible controls. This set is then shown to be contained in
the original nonconvex set of feasible controls, thereby estab-
lishing that we can obtain optimal solutions of the original
nonconvex problem via solving its convex relaxation."