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A class of two-parameter Poisson-Dirichlet distributions have non-vanishing coefficient of variation. This phenomenon is also known as non-self averaging stochastic multi-sector endogenous growth model. This model is used to raise questions on the use of means in assessing effectiveness of macroeconomic or other macro-policy effects. The coefficients of variations of the number of total sectors, and...
System design in presence of uncertainty calls for experimentation, and a question that arises naturally is: how many experiments are needed to come up with a system meeting certain performance requirements? This contribution represents an attempt to answer this fundamental question. Results are con- fined to a specific set-up where adaptation is performed according to a worst-case perspective,...
In this paper a new distance on the set of multivariate Gaussian linear stochastic processes is proposed based on the notion of mutual information. The definition of the distance is inspired by various properties of the mutual information of past and future of a stochastic process. For two special classes of stochastic processes this mutual information distance is shown to be equal to a cepstral distance...
One of the modern geometric views of dynamical systems is as vector fields on a manifold, with or without boundary. The starting point of this paper is the observation that, since one-forms are the natural expression of linear functionals on the space of vector fields, the interaction between the two makes some aspects of the study of equilibria and periodic orbits more tractable, at least in certain...
Graphical models in which every node holds a time-series were analysed in Caines et al. [13], [14] using the notion of lattice conditional independence (LCI) due to Anderson et al. [1], [2]. Under certain feedback free (or causality) conditions, LCI imposes a special zero structure on the stochastic realizations of those processes generated by state space systems; this structure comes directly from...
System identification is concerned with obtaining good models from data, i.e. with data driven modeling. In this contribution the aim is to explain and discuss ideas, general approaches and theories underlying identification of linear systems. Identification of linear systems is a nonlinear problem and is “prototypical” also for many parts of identification of nonlinear systems.
In this paper, we consider the problem of finding, among solutions of a moment problem, the best Kullback-Leibler approximation of a given a priori spectral density. We present a new complete existence proof for the dual optimization problem in the Byrnes-Lindquist spirit. We also prove a descent property for a matricial iterative method for the numerical solution of the dual problem. The latter has...
Factor analysis, in its original formulation, deals with the linear statistical model 1 $$ Y = HX + \varepsilon $$ where H is a deterministic matrix, X and ge independent random vectors, the first with dimension smaller than Y, the second with independent components. What makes this model attractive in applied research is the data reduction mechanism built in it. A large number of observed variables...
The theme of the present paper is the study of two different versions of tensor products of functional models and present some applications to various problems related to system theory. Among those are stability of higher order systems, tangent spaces, spaces of intertwining maps, invariant factors of tensor products of linear transformations and the solvability of Sylvester equations.
We begin with an interpretation of the L1-distance between two power spectral densities and then, following an analogous rationale, we develop a natural metric for quantifying distance between respective covariance matrices.
It is a typical situation in modern modeling that a total model is built up from simpler submodels, or modules, for example residing in a model library. The total model could be quite complex, while the modules are well understood and analysed. A procedure to decide global parameter identifiability for such a collection of model equations of differential-algebraic nature is suggested. It is shown...
We consider hidden Markov processes in discrete time with a finite state space X and a general observation or read-out space Y. The identification of the unknown dynamics is carried out by the conditional maximum-likelihood method. The normalized log-likelihood function is shown to satisfy a uniform law of large numbers over certain compact subsets of the parameter space. Two cases are covered: first,...
This chapter takes a new look at the concept of identifiability and of informative experiments for linear time-invariant systems, both in open-loop and in closed-loop identification. Some readers might think that everything has been said and written about these concepts, which were much studied all through the 1970’s. We shared the same view ... until recently. The motivation for our renewed interest...
We show how the Kimura-Georgiou parametrization for interpolating a function and its derivatives at 0 is independent of the particular choice of basis of Szegö-polynomials of first and second kind, but only on the map between these two polynomial bases. This leads to a more general parametrization, which extends to different interpolation points and multivariable setup.
Differential equations are types of equations that arise from the mathematical modelling, or simulation, of physical phenomena or from engineering applications; for example: the flow of water, the decay of radioactive substances, bodies in motion, electrical circuits, chemical processes, etc. When we cannot solve differential equations analytically, we must resort to numerical methods. Unfortunately,...
In this paper a recursive smoothing spline approach is used for reconstructing a closed contour. Periodic splines are generated through minimizing a cost function subject to constraints imposed by a linear control system. The filtering effect of the smoothing splines allows for usage of noisy sensor data. An important feature of the method is that several data sets for the same closed contour can...
We revisit the deterministic subspace identification methods for discrete-time LTI systems, and show that each column vector of the L-matrix of the LQ decomposition in MOESP and N4SID methods is a pair of input-output vectors formed by linear combinations of given input-output data. Thus, under the assumption that the input is persistently exciting (PE) of sufficient order, we can easily compute zero-input...
This paper studies canonical operators on finite graphs, with the aim of characterizing the toolbox of linear feedback laws available to control networked dynamical systems.
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