189 research outputs found
On the notion of conductor in the local geometric Langlands correspondence
Under the local Langlands correspondence, the conductor of an irreducible
representation of \Gl_n(F) is greater than the Swan conductor of the
corresponding Galois representation. In this paper, we establish the geometric
analogue of this statement by showing that the conductor of a categorical
representation of the loop group is greater than the irregularity of the
corresponding meromorphic connection.Comment: Minor report following referees report. To appear in Canadian Journal
of Mat
Unified Approach to Convex Robust Distributed Control given Arbitrary Information Structures
We consider the problem of computing optimal linear control policies for
linear systems in finite-horizon. The states and the inputs are required to
remain inside pre-specified safety sets at all times despite unknown
disturbances. In this technical note, we focus on the requirement that the
control policy is distributed, in the sense that it can only be based on
partial information about the history of the outputs. It is well-known that
when a condition denoted as Quadratic Invariance (QI) holds, the optimal
distributed control policy can be computed in a tractable way. Our goal is to
unify and generalize the class of information structures over which quadratic
invariance is equivalent to a test over finitely many binary matrices. The test
we propose certifies convexity of the output-feedback distributed control
problem in finite-horizon given any arbitrarily defined information structure,
including the case of time varying communication networks and forgetting
mechanisms. Furthermore, the framework we consider allows for including
polytopic constraints on the states and the inputs in a natural way, without
affecting convexity
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