5,609 research outputs found
Integral and measure-turnpike properties for infinite-dimensional optimal control systems
We first derive a general integral-turnpike property around a set for
infinite-dimensional non-autonomous optimal control problems with any possible
terminal state constraints, under some appropriate assumptions. Roughly
speaking, the integral-turnpike property means that the time average of the
distance from any optimal trajectory to the turnpike set con- verges to zero,
as the time horizon tends to infinity. Then, we establish the measure-turnpike
property for strictly dissipative optimal control systems, with state and
control constraints. The measure-turnpike property, which is slightly stronger
than the integral-turnpike property, means that any optimal (state and control)
solution remains essentially, along the time frame, close to an optimal
solution of an associated static optimal control problem, except along a subset
of times that is of small relative Lebesgue measure as the time horizon is
large. Next, we prove that strict strong duality, which is a classical notion
in optimization, implies strict dissipativity, and measure-turnpike. Finally,
we conclude the paper with several comments and open problems
Nakayama automorphisms of double Ore extensions of Koszul regular algebras
Let be a Koszul Artin-Schelter regular algebra and an algebra
homomorphism from to . We compute the Nakayama
automorphisms of a trimmed double Ore extension
(introduced in \cite{ZZ08}). Using a similar method, we also obtain the
Nakayama automorphism of a skew polynomial extension , where
is a graded algebra automorphism of . These lead to a
characterization of the Calabi-Yau property of , the
skew Laurent extension and with a diagonal type.Comment: The paper has been heavily revised including the title, and will
appear in Manuscripta Mathematic
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