207 research outputs found
H_2-Optimal Decentralized Control over Posets: A State-Space Solution for State-Feedback
We develop a complete state-space solution to H_2-optimal decentralized
control of poset-causal systems with state-feedback. Our solution is based on
the exploitation of a key separability property of the problem, that enables an
efficient computation of the optimal controller by solving a small number of
uncoupled standard Riccati equations. Our approach gives important insight into
the structure of optimal controllers, such as controller degree bounds that
depend on the structure of the poset. A novel element in our state-space
characterization of the controller is a remarkable pair of transfer functions,
that belong to the incidence algebra of the poset, are inverses of each other,
and are intimately related to prediction of the state along the different paths
on the poset. The results are illustrated by a numerical example.Comment: 39 pages, 2 figures, submitted to IEEE Transactions on Automatic
Contro
Optimal Output Feedback Architecture for Triangular LQG Problems
Distributed control problems under some specific information constraints can
be formulated as (possibly infinite dimensional) convex optimization problems.
The underlying motivation of this work is to develop an understanding of the
optimal decision making architecture for such problems. In this paper, we
particularly focus on the N-player triangular LQG problems and show that the
optimal output feedback controllers have attractive state space realizations.
The optimal controller can be synthesized using a set of stabilizing solutions
to 2N linearly coupled algebraic Riccati equations, which turn out to be easily
solvable under reasonable assumptions.Comment: To be presented at 2014 American Control Conferenc
Weighted -minimization for generalized non-uniform sparse model
Model-based compressed sensing refers to compressed sensing with extra
structure about the underlying sparse signal known a priori. Recent work has
demonstrated that both for deterministic and probabilistic models imposed on
the signal, this extra information can be successfully exploited to enhance
recovery performance. In particular, weighted -minimization with
suitable choice of weights has been shown to improve performance in the so
called non-uniform sparse model of signals. In this paper, we consider a full
generalization of the non-uniform sparse model with very mild assumptions. We
prove that when the measurements are obtained using a matrix with i.i.d
Gaussian entries, weighted -minimization successfully recovers the
sparse signal from its measurements with overwhelming probability. We also
provide a method to choose these weights for any general signal model from the
non-uniform sparse class of signal models.Comment: 32 Page
Solving Commutative Relaxations of Word Problems
We present an algebraic characterization of the standard commutative relaxation of the word problem in terms of a polynomial equality. We then consider a variant of the
commutative word problem, referred to as the “Zero-to-All
reachability” problem. We show that this problem is equivalent to a finite number of commutative word problems, and we use this insight to derive necessary conditions for Zero-to-All reachability. We conclude with a set of illustrative examples
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