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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 be processed recursively so that the accuracy can be improved meanwhile the current mapping can be used for planning the path for the data-collecting robot. [ABSTRACT FROM AUTHOR]

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 and zero-state responses by appropriately dividing given input-output data into past and future in the LQ decomposition. This reveals the role of the LQ decomposition in subspace identification methods. Also, a related issue in stochastic realization is briefly discussed in Appendix. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Subspace System Identification is by now an established methodology for experimental modelling. The basic theory is well understood and it is more or less a standard tool in industry. The two main research problems in subspace system identification that have been studied in the recent years are closed loop system identification and performance analysis. The aim of this contribution is quite different. We have asked an industrial expert working in process control a set of questions on how subspace system identification is used in design of model predictive control systems for process industry. As maybe expected, it turns out that a main issue is experiment/input design. Here, the difference between theory and practice is rather large mainly due to implementation constraints, but also lack of knowledge transfer. Motivated by the response from the expert, we will discuss several important user choices problems, such as optimal input design, merging of data sets and merging of models. [ABSTRACT FROM AUTHOR]

It is a great pleasure to contribute this article to the special issue in honor of Giorgio Picci on the occasion of his 65th birthday. Throughout his career, stochastic methods in modeling and filtering have been central to Giorgio's research. This article intends to describe a new idea in digital filter design, but from a deterministic point of view. I hope that it can provide a contrasting viewpoint on noise and signals in some specific contexts. [ABSTRACT FROM AUTHOR]

An algorithm is presented for the computation of the most powerful unfalsified model associated with an observed vector time series in the class of dynamical systems described by linear constant coefficient difference equations. This algorithm computes a module basis of the left kernel the Hankel matrix of the data, and is recursive in the elements of the basis. It is readily combined with subspace identification ideas, in which a state trajectory is computed first, directly from the data, and the parameters of the identified model are derived from the state trajectory. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present a novel way to formulate control problems with partial observations of stochastic systems. Themethod is based on stochastic realization theory. The contribution of the paper is the stochastic realization approach to stochastic control with partial observations. The motivation for the paper are the weaknesses of control with partial observations based on the separation principle. The separation property holds for the stochastic control problem with a Gaussian system and a quadratic cost function (LQG), but does not hold for at least one optimal stochastic control problem, LEQG, and may not hold for most other stochastic control problems. Moreover, control of decentralized stochastic systems or control of stochastic dynamic games becomes unsolvable or unnatural in the existing approaches in the literature. Therefore a novel approach may be explored. [ABSTRACT FROM AUTHOR]

Comparing time series is a problem of critical importance in a broad range of applications, from data mining (searching for temporal "patterns" in historical data), to speech recognition (classifying phonemes from acoustic recordings), surveillance (detecting unusual events from video and other sensory input), computer animation (concatenating and interpolating motion capture sequences), just to mention a few. The problem is difficult because the same event can manifest itself in a variety of ways, with the data subject to a large degree of variability due to nuisance factors in the data formation process. For instance, the presence of a person walking in a video sequence can vary based on the individual, his gait, location, orientation, speed, clothing, illumination etc. And yet, if I see Giorgio Picci, I can recognize him from one hundred yards away by the way he walks, regardless of what he is wearing, or whether it is a sunny or a cloudy day. One could conjecture that there must exist some statistics of my retinal signals that are invariant, or at least insensitive, to such nuisance factors and are instead Giorgio-Specific (GS). The information ought to be encoded in the temporal evolution of the retinal signals, for one can strip the images of their pictorial content by attaching light bulbs to one's joints and turning off the lights (or use a state-of-the-art motion capture system, for instance one made by E-motion/BTS); one can still tell a great deal from just the moving dots [6]. [ABSTRACT FROM AUTHOR]

In this chapter we look at a geometric target assignment problem consisting of an equal number of mobile robotic agents and distinct target locations. Each agent has a fixed communication range, a maximum speed, and knowledge of every target's position. The problem is to devise a distributed algorithm that allows the agents to divide the target locations among themselves and, simultaneously, leads each agent to its unique target. We summarize two algorithms for this problem; one designed for "sparse" environments, in which communication between robots is sparse, and one for "dense" environments, where communication is more prevalent. We characterize the asymptotic performance of these algorithms as the number of agents increases and the environment grows to accommodate them. [ABSTRACT FROM AUTHOR]

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 how to make use of the natural modularization of the model structure. Basically, global identifiability is obtained if and only if each module is identifiable, and the connecting signals can be retrieved from the external signals, without knowledge of the values of the parameters. [ABSTRACT FROM AUTHOR]

This paper is dedicated to Giorgio Picci on the occasion of his 65th birthday. I have come to appreciate Giorgio not only as a great friend but also as a great scholar. When we first met at Brown University in 1973, he introduced me to his seminal paper [29] on splitting subspaces, which became the impetus for our joint work on the geometric theory of linear stochastic systems [23,24,25,26]. This led to a life-long friendship and a book project that never seemed to converge, but now is close to being finished [27]. I have learned a lot from Giorgio. The present paper grew out of a discussion in our book project, when Giorgio taught me about the connections between prediction-error identification and the Kullback-Leibler criterion. These concepts led directly into the recent theory of analytic interpolation with complexity constraint, with which I have been deeply involved in recent times. I shall try to explain these connections in the following paper [ABSTRACT FROM AUTHOR]

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 into these very fundamental questions is the recent surge of interest in the question of experiment design, itself triggered by the new concept of least costly identification experiment for robust control [3, 4, 5, 6]. Briefly speaking, least costly experiment design for robust control refers to achieving a prescribed accuracy at the lowest possible price, which is typically measured in terms of the duration of the identification experiment, the perturbation induced by the excitation signal, or any combination of these. [ABSTRACT FROM AUTHOR]

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, numerical methods do not give us an exact solution, and an amount of error is introduced in the answer. It is our goal to utilize concepts from Control Theory in order to minimize this error. For our study, we shall focus on ordinary differential equations (ODEs). [ABSTRACT FROM AUTHOR]

We consider hidden Markov processes in discrete time with a finite state space $\cal X$ and a general observation or read-out space $\cal Y$. 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, when the running value of the transition probability matrix, denoted by Q is positive, second, when Q is primitive, but the read-out densities are strictly positive. [ABSTRACT FROM AUTHOR]

Factor analysis, in its original formulation, deals with the linear statistical model $$Y = HX + \epsilon $$ where H is a deterministic matrix, X and ε 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 Y are explained in terms of a small number of unobserved (latent) variables X perturbed by the independent noise ∈. Under normality assumptions, which are the rule in the standard theory, all the laws of the model are specified by covariance matrices. More precisely, assume that X and ε are zero mean independent normal vectors with ℂov(X) = P and ℂov (ε) = D, where D is diagonal. It follows from ([1]) that ℂov(Y) = HPHT + D. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 proven to perform extremely well in simulation testbeds. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 the transitive directed acyclic graph (TDAG) which is in one-to-one correspondence with the Boolean Hilbert lattice of the LCI formulation. In this paper, these properties of sets of stochastic processes are generalized to the setting of infinite Bayes nets of time series; this formulation contains as a special case conditionally independent processes embedded in chain recurrent spatial structures. [ABSTRACT FROM AUTHOR]

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 confined to a specific set-up where adaptation is performed according to a worst-case perspective, but many considerations and reflections are central to adaptation in general. [ABSTRACT FROM AUTHOR]

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. For general multivariate processes, the behavior of the mutual information distance is similar to the behavior of an ad hoc defined multivariate cepstral distance. [ABSTRACT FROM AUTHOR]

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 cases. [ABSTRACT FROM AUTHOR]

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 of sectors of a given size all remain positive as the model size grows unboundedly. [ABSTRACT FROM AUTHOR]