52 research outputs found
On the existence of a solution to a spectral estimation problem \emph{\`a la} Byrnes-Georgiou-Lindquist
A parametric spectral estimation problem in the style of Byrnes, Georgiou,
and Lindquist was posed in \cite{FPZ-10}, but the existence of a solution was
only proved in a special case. Based on their results, we show that a solution
indeed exists given an arbitrary matrix-valued prior density. The main tool in
our proof is the topological degree theory.Comment: 6 pages of two-column draft, accepted for publication in IEEE-TA
On Minimal Spectral Factors with Zeroes and Poles lying on Prescribed Region
In this paper, we consider a general discrete-time spectral factorization
problem for rational matrix-valued functions. We build on a recent result
establishing existence of a spectral factor whose zeroes and poles lie in any
pair of prescribed regions of the complex plane featuring a geometry compatible
with symplectic symmetry. In this general setting, uniqueness of the spectral
factor is not guaranteed. It was, however, conjectured that if we further
impose stochastic minimality, uniqueness can be recovered. The main result of
his paper is a proof of this conjecture.Comment: 14 pages, no figures. Revised version with minor modifications. To
appear in IEEE Transactions of Automatic Contro
Quantum State Preparation by Controlled Dissipation in Finite Time: From Classical to Quantum Controllers
We propose a general scheme for dissipatively preparing arbitrary pure
quantum states on a multipartite qubit register in a finite number of basic
control blocks. Our "splitting-subspace" approach relies on control resources
that are available in a number of scalable quantum technologies (complete
unitary control on the target system, an ancillary resettable qubit and
controlled-not gates between the target and the ancilla), and can be seen as a
"quantum-controller" implementation of a sequence of classical feedback loops.
We show how a large degree of flexibility exists in engineering the required
conditional operations, and make explicit contact with a stabilization protocol
used for dissipative quantum state preparation and entanglement generation in
recent experiments with trapped ions.Comment: 10 pages, 2 figures. Submitted to CDC 201
A Framework to Control Functional Connectivity in the Human Brain
In this paper, we propose a framework to control brain-wide functional
connectivity by selectively acting on the brain's structure and parameters.
Functional connectivity, which measures the degree of correlation between
neural activities in different brain regions, can be used to distinguish
between healthy and certain diseased brain dynamics and, possibly, as a control
parameter to restore healthy functions. In this work, we use a collection of
interconnected Kuramoto oscillators to model oscillatory neural activity, and
show that functional connectivity is essentially regulated by the degree of
synchronization between different clusters of oscillators. Then, we propose a
minimally invasive method to correct the oscillators' interconnections and
frequencies to enforce arbitrary and stable synchronization patterns among the
oscillators and, consequently, a desired pattern of functional connectivity.
Additionally, we show that our synchronization-based framework is robust to
parameter mismatches and numerical inaccuracies, and validate it using a
realistic neurovascular model to simulate neural activity and functional
connectivity in the human brain.Comment: To appear in the proceedings of the 58th IEEE Conference on Decision
and Contro
On the Factorization of Rational Discrete-Time Spectral Densities
In this paper, we consider an arbitrary matrix-valued, rational spectral
density . We show with a constructive proof that admits a
factorization of the form , where is
stochastically minimal. Moreover, and its right inverse are analytic in
regions that may be selected with the only constraint that they satisfy some
symplectic-type conditions. By suitably selecting the analyticity regions, this
extremely general result particularizes into a corollary that may be viewed as
the discrete-time counterpart of the matrix factorization method devised by
Youla in his celebrated work (Youla, 1961).Comment: 34 pages, no figures. Revised version with partial rewriting of
Section I and IV, added Section VI with a numerical example and other minor
changes. To appear in IEEE Transactions of Automatic Contro
Novel Results on the Factorization and Estimation of Spectral Densities
This dissertation is divided into two main parts. The first part is concerned with one of the most classical and central problems in Systems and Control Theory, namely the factorization of rational matrix-valued spectral densities, commonly known as the spectral factorization problem. Spectral factorization is a fundamental tool for the solution of a variety of problems involving second-order statistics and quadratic cost functions in control, estimation, signal processing and communications. It can be thought of as the frequency-domain counterpart of the ubiquitous Algebraic Riccati Equation and it is intimately connected with the celebrated Kálmán-Yakubovich-Popov Lemma and, therefore, to passivity theory. Here, we provide a rather in-depth and comprehensive analysis of this problem in the discrete-time setting, a scenario which is becoming increasingly pervasive in control applications. The starting point in our analysis is a general spectral factorization result in the same vein of Dante C. Youla. Building on this fundamental result, we then investigate some key issues related to minimality and parametrization of minimal spectral factors of a given spectral density. To conclude, we show how to extend some of the ideas and results to the more general indefinite or J-spectral factorization problem, a technique of paramount importance in robust control and estimation theory.
In the second part of the dissertation, we consider the problem of estimating a spectral density from a finite set of measurements. Following the Byrnes-Georgiou-Lindquist THREE (Tunable High REsolution Estimation) paradigm, we look at spectral estimation as an optimization problem subjected to a generalized moment constraint. In this framework, we examine the global convergence of an efficient algorithm for the estimation of scalar spectral densities that hinges on the Kullback-Leibler criterion. We then move to the multivariate setting by addressing the delicate issue of existence of solutions to a parametric spectral estimation problem. Eventually, we study the geometry of the space of spectral densities by revisiting two natural distances defined in cones for the case of rational spectra. These new distances are used to formulate a "robust" version of THREE-like spectral estimation
Conal Distances Between Rational Spectral Densities
This paper generalizes Thompson and Hilbert
metrics to the space of spectral densities. The resulting
complete metric space has the differentiable structure of a
Finsler manifold with explicit geodesics. The corresponding distances are filtering invariant, can be computed efficiently, and admit geodesic paths that preserve rationality; these are properties of fundamental importance in many
engineering applications.European Research Counci
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