Consensus State Gram Matrix Estimation for Stochastic Switching Networks from Spectral Distribution Moments

Reaching distributed average consensus quickly and accurately over a network through iterative dynamics represents an important task in numerous distributed applications. Suitably designed filters applied to the state values can significantly improve the convergence rate. For constant networks, these filters can be viewed in terms of graph signal processing as polynomials in a single matrix, the consensus iteration matrix, with filter response evaluated at its eigenvalues. For random, time-varying networks, filter design becomes more complicated, involving eigendecompositions of sums and products of random, time-varying iteration matrices. This paper focuses on deriving an estimate for the Gram matrix of error in the state vectors over a filtering window for large-scale, stationary, switching random networks. The result depends on the moments of the empirical spectral distribution, which can be estimated through Monte-Carlo simulation. This work then defines a quadratic objective function to minimize the expected consensus estimate error norm. Simulation results provide support for the approximation.Comment: 52nd Asilomar Conference on Signals, Systems, and Computers (Asilomar 2017

Testing for Cointegration with Nonstationary Volatility

The paper generalises recent unit root tests for nonstationary volatility to a multivariate context. Persistent changes in the innovation variance matrix lead to size distortions in conventional cointegration tests, and possibilities of increased power by taking the time-varying volatilities and correlations into account. The testing procedures are based on a likelihood analysis of the vector autoregressive model with a conditional covariance matrix that may be estimated nonparametrically. We find that under suitable conditions, adaptation with respect to the volatility matrix process is possible, in the sense that nonparametric volatility estimation does not lead to a loss of asymptotic local power

Nonlinear adaptive estimation with application to sinusoidal identification

Parameter estimation of a sinusoidal signal in real-time is encountered in applications in numerous areas of engineering. Parameters of interest are usually amplitude, frequency and phase wherein frequency tracking is the fundamental task in sinusoidal estimation. This thesis deals with the problem of identifying a signal that comprises n (n ≥ 1) harmonics from a measurement possibly affected by structured and unstructured disturbances. The structured perturbations are modeled as a time-polynomial so as to represent, for example, bias and drift phenomena typically present in applications, whereas the unstructured disturbances are characterized as bounded perturbation. Several approaches upon different theoretical tools are presented in this thesis, and classified into two main categories: asymptotic and non-asymptotic methodologies, depending on the qualitative characteristics of the convergence behavior over time. The first part of the thesis is devoted to the asymptotic estimators, which typically consist in a pre-filtering module for generating a number of auxiliary signals, independent of the structured perturbations. These auxiliary signals can be used either directly or indirectly to estimate—in an adaptive way—the frequency, the amplitude and the phase of the sinusoidal signals. More specifically, the direct approach is based on a simple gradient method, which ensures Input-to-State Stability of the estimation error with respect to the bounded-unstructured disturbances. The indirect method exploits a specific adaptive observer scheme equipped with a switching criterion allowing to properly address in a stable way the poor excitation scenarios. It is shown that the adaptive observer method can be applied for estimating multi-frequencies through an augmented but unified framework, which is a crucial advantage with respect to direct approaches. The estimators’ stability properties are also analyzed by Input-to-State-Stability (ISS) arguments. In the second part we present a non-asymptotic estimation methodology characterized by a distinctive feature that permits finite-time convergence of the estimates. Resorting to the Volterra integral operators with suitably designed kernels, the measured signal is processed, yielding a set of auxiliary signals, in which the influence of the unknown initial conditions is annihilated. A sliding mode-based adaptation law, fed by the aforementioned auxiliary signals, is proposed for deadbeat estimation of the frequency and amplitude, which are dealt with in a step-by-step manner. The worst case behavior of the proposed algorithm in the presence of bounded perturbation is studied by ISS tools. The practical characteristics of all estimation techniques are evaluated and compared with other existing techniques by extensive simulations and experimental trials.Open Acces

Adaptive multigrid domain decomposition solutions for viscous interacting flows

Several viscous incompressible flows with strong pressure interaction and/or axial flow reversal are considered with an adaptive multigrid domain decomposition procedure. Specific examples include the triple deck structure surrounding the trailing edge of a flat plate, the flow recirculation in a trough geometry, and the flow in a rearward facing step channel. For the latter case, there are multiple recirculation zones, of different character, for laminar and turbulent flow conditions. A pressure-based form of flux-vector splitting is applied to the Navier-Stokes equations, which are represented by an implicit lowest-order reduced Navier-Stokes (RNS) system and a purely diffusive, higher-order, deferred-corrector. A trapezoidal or box-like form of discretization insures that all mass conservation properties are satisfied at interfacial and outflow boundaries, even for this primitive-variable, non-staggered grid computation

Robustness, Weak Stability, and Stability in Distribution of Adaptive Filteringalgorithms Under Model Mismatch

This work is concerned with robustness, convergence, and stability of adaptive filtering (AF) type algorithms in the presence of model mismatch. The algorithms under consideration are recursive and have inherent multiscale structure. They can be considered as dynamic systems, in which the `state\u27 changes much more slowly than the perturbing noise. Beyond the existing results on adaptive algorithms, model mismatch significantly affects convergence properties of AF algorithms, raising issues of algorithm robustness. Weak convergence and weak stability (i.e., recurrence) under model mismatch are derived. Based on the limiting stochastic differential equations of suitably scaled iterates, stability in distribution is established. Then algorithms with decreasing step sizes and their convergence properties are examined. When input signals are large, identification bias due to model mismatch will become large and unacceptable. Methods for reducing such bias are introduced when the identified models are used in regulation problems