Results 1  10
of
87
Synchronization and linearity: an algebra for discrete event systems
, 2001
"... The first edition of this book was published in 1992 by Wiley (ISBN 0 471 93609 X). Since this book is now out of print, and to answer the request of several colleagues, the authors have decided to make it available freely on the Web, while retaining the copyright, for the benefit of the scientific ..."
Abstract

Cited by 250 (10 self)
 Add to MetaCart
The first edition of this book was published in 1992 by Wiley (ISBN 0 471 93609 X). Since this book is now out of print, and to answer the request of several colleagues, the authors have decided to make it available freely on the Web, while retaining the copyright, for the benefit of the scientific community. Copyright Statement This electronic document is in PDF format. One needs Acrobat Reader (available freely for most platforms from the Adobe web site) to benefit from the full interactive machinery: using the package hyperref by Sebastian Rahtz, the table of contents and all LATEX crossreferences are automatically converted into clickable hyperlinks, bookmarks are generated automatically, etc.. So, do not hesitate to click on references to equation or section numbers, on items of thetableofcontents and of the index, etc.. One may freely use and print this document for one’s own purpose or even distribute it freely, but not commercially, provided it is distributed in its entirety and without modifications, including this preface and copyright statement. Any use of thecontents should be acknowledged according to the standard scientific practice. The
Basic problems in stability and design of switched systems
 IEEE Control Systems Magazine
, 1999
"... By a switched system, we mean a hybrid dynamical system consisting of a family of continuoustime subsystems and a rule that orchestrates the switching between them. This article surveys recent developments in three basic problems regarding stability and design of switched systems. These problems ar ..."
Abstract

Cited by 206 (9 self)
 Add to MetaCart
By a switched system, we mean a hybrid dynamical system consisting of a family of continuoustime subsystems and a rule that orchestrates the switching between them. This article surveys recent developments in three basic problems regarding stability and design of switched systems. These problems are: stability for arbitrary switching sequences, stability for certain useful classes of switching sequences, and construction of stabilizing switching sequences. We also provide motivation for studying these problems by discussing how they arise in connection with various questions of interest in control theory and applications.
Quantized Feedback Stabilization of Linear Systems
 IEEE Trans. Automat. Control
, 2000
"... This paper addresses feedback stabilization problems for linear timeinvariant control systems with saturating quantized measurements. We propose a new control design methodology, which relies on the possibility of changing the sensitivity of the quantizer while the system evolves. The equation that ..."
Abstract

Cited by 163 (23 self)
 Add to MetaCart
This paper addresses feedback stabilization problems for linear timeinvariant control systems with saturating quantized measurements. We propose a new control design methodology, which relies on the possibility of changing the sensitivity of the quantizer while the system evolves. The equation that describes the evolution of the sensitivity with time (discrete rather than continuous in most cases) is interconnected with the given system (either continuous or discrete), resulting in a hybrid system. When applied to systems that are stabilizable by linear timeinvariant feedback, this approach yields global asymptotic stability. Index TermsFeedback stabilization, hybrid system, linear control system, quantized measurement. I. INTRODUCTION T HIS PAPER deals with quantized feedback stabilization problems for linear timeinvariant control systems. A quantizer, as defined here, acts as a functional that maps a realvalued function into a piecewise constant function taking on a finite...
A note on the stochastic realization problem
 Hemisphere Publishing Corporation
, 1976
"... Abstract. Given a mean square continuous stochastic vector process y with stationary increments and a rational spectral density such that (oo) is finite and nonsingular, consider the problem of finding all minimal (wide sense) Markov representations (stochastic realizations) of y. All such realizati ..."
Abstract

Cited by 98 (23 self)
 Add to MetaCart
Abstract. Given a mean square continuous stochastic vector process y with stationary increments and a rational spectral density such that (oo) is finite and nonsingular, consider the problem of finding all minimal (wide sense) Markov representations (stochastic realizations) of y. All such realizations are characterized and classified with respect to deterministic as well as probabilistic properties. It is shown that only certain realizations (internal stochastic realizations) can be determined from the given output process y. All others (external stochastic realizations)require that the probability space be extended with an exogeneous random component. A complete characterization of the sets of internal and external stochastic realizations is provided. It is shown that the state process of any internal stochastic realization can be expressed in terms of two steadystate KalmanBucy filters, one evolving forward in time over the infinite past and one backward over the infinite future. An algorithm is presented which generates families Of external realizations defined on the same probability space and totally ordered with respect to state covariances. 1. Introduction. One
Contributions to the Theory of Optimal Control
, 1960
"... This paper was in fact the first to introduce the RDE as an algorithm for computing the state feedback gain of the optimal controller for a general linear system with a quadratic performance criterion. RDE had emerged earlier in the study of the second variations in the calculus of variations, but i ..."
Abstract

Cited by 60 (1 self)
 Add to MetaCart
This paper was in fact the first to introduce the RDE as an algorithm for computing the state feedback gain of the optimal controller for a general linear system with a quadratic performance criterion. RDE had emerged earlier in the study of the second variations in the calculus of variations, but its use in general linear systems, where the optimal trajectory needs to be generated by a control input, was new. The analysis throughout the paper concentrates on timevarying systems, and uses the HamiltonJacobi theory to arrive at RDE and to deduce optimality of the LQ control gain. We now know, however, that an alternative way to prove optimality in least squares is by showing how RDE allows one to "complete the square" (see, e.g., [5], [18]).
An overview of process query systems
 In Proceedings of SPIE Vol. 5403 Sensors, and Command, Control, Communications, and Intelligence (C3I) Technologies for Homeland Security and Homeland Defense III
, 2004
"... Sensors produce large streams of raw events while instrumenting environments such as computer systems, communications networks, physical spaces, and human organizations. Extracting meaningful and actionable information from these events, however, remains a challenge. Process query systems, a new alg ..."
Abstract

Cited by 23 (13 self)
 Add to MetaCart
Sensors produce large streams of raw events while instrumenting environments such as computer systems, communications networks, physical spaces, and human organizations. Extracting meaningful and actionable information from these events, however, remains a challenge. Process query systems, a new algorithmic and software paradigm, offer a powerful and generic way to address eventprocessing challenges. Our ability to instrument different environments has increased dramatically in recent years. Computer systems and networks now routinely include various performance monitors, firewalls, intrusiondetection systems, and applicationlogging agents. Researchers can deploy sensor networks in physical environments to record acoustic, seismic, infrared, video, electromagnetic, and other types of measurements. These networks also can monitor and extensively archive communications and financial and social transactions among large communities of people and organizations. We now have a tremendous amount of data coming at us; the question remains what to do with it. Generally speaking, the underlying purpose of instrumenting environments is to better understand “what is going on, ” formally known as situational awareness. In the context of computer security, situational awareness typically means knowing which monitored systems are under attack and the nature of those attacks. For a physical sensor network within a building or extending across a geographic region, this might mean being cognizant of certain objects and activities, such as a fire, people, animals, or vehicles and their location. In industrial and manufacturing systems, situational awareness means detecting infrastructure failures and diagnosing their causes.
Dissipation induced instabilities
 Ann. Inst. Henri Poincar'e
, 1994
"... The main goal of this paper is to prove that if the energymomentum (or energyCasimir) methodpredicts formal instability of a relative equilibrium in a Hamiltonian system with symmetry, then with the addition of dissipation, the relative equilibrium becomes spectrally andhence linearly andnonlinear ..."
Abstract

Cited by 21 (12 self)
 Add to MetaCart
The main goal of this paper is to prove that if the energymomentum (or energyCasimir) methodpredicts formal instability of a relative equilibrium in a Hamiltonian system with symmetry, then with the addition of dissipation, the relative equilibrium becomes spectrally andhence linearly andnonlinearly unstable. The energymomentum methodassumes that one is in the context of a mechanical system with a given symmetry group. Our result assumes that the dissipation chosen does not destroy the conservation law associated with the given symmetry group—thus, we consider internal dissipation. This also includes the special case of systems with no symmetry and ordinary equilibria. The theorem is provedby combining the techniques of Chetaev, who proved instability theorems using a special ChetaevLyapunov function, with those of
Passivity Enforcement via Perturbation of Hamiltonian Matrices
 IEEE TRANS. CASI
, 2004
"... This paper presents a new technique for the passivity enforcement of linear timeinvariant multiport systems in statespace form. This technique is based on a study of the spectral properties of related Hamiltonian matrices. The formulation is applicable in case the system inputoutput transfer func ..."
Abstract

Cited by 18 (4 self)
 Add to MetaCart
This paper presents a new technique for the passivity enforcement of linear timeinvariant multiport systems in statespace form. This technique is based on a study of the spectral properties of related Hamiltonian matrices. The formulation is applicable in case the system inputoutput transfer function is in admittance, impedance, hybrid, or scattering form. A standard test for passivity is first performed by checking the existence of imaginary eigenvalues of the associated Hamiltonian matrix. In the presence of imaginary eigenvalues the system is not passive. In such a case, a new result based on firstorder perturbation theory is presented for the precise characterization of the frequency bands where passivity violations occur. This characterization is then used for the design of an iterative perturbation scheme of the state matrices, aimed at the displacement of the imaginary eigenvalues of the Hamiltonian matrix. The result is an effective algorithm leading to the compensation of the passivity violations. This procedure is very efficient when the passivity violations are small, so that firstorder perturbation is applicable. Several examples illustrate and validate the procedure.
Classification and recognition of dynamical models: the role of phase, independent components, kernels and optimal transport
 IEEE Trans. Pattern Anal. Mach. Intell
, 2007
"... Abstract—We address the problem of performing decision tasks and, in particular, classification and recognition in the space of dynamical models in order to compare time series of data. Motivated by the application of recognition of human motion in image sequences, we consider a class of models that ..."
Abstract

Cited by 18 (4 self)
 Add to MetaCart
Abstract—We address the problem of performing decision tasks and, in particular, classification and recognition in the space of dynamical models in order to compare time series of data. Motivated by the application of recognition of human motion in image sequences, we consider a class of models that include linear dynamics, both stable and marginally stable (periodic), both minimum and nonminimum phases, driven by nonGaussian processes. This requires extending existing learning and system identification algorithms to handle periodic modes and nonminimumphase behavior while taking into account higher order statistics of the data. Once a model is identified, we define a kernelbased cord distance between models, which includes their dynamics, their initial conditions, and input distribution. This is made possible by a novel kernel defined between two arbitrary (nonGaussian) distributions, which is computed by efficiently solving an optimal transport problem. We validate our choice of models, inference algorithm, and distance on the tasks of human motion synthesis (sample paths of the learned models) and recognition (nearestneighbor classification in the computed distance). However, our work can be applied more broadly where one needs to compare historical data while taking into account periodic trends, nonminimumphase behavior, and nonGaussian input distributions.
Structural Stability of Turbulent Jets
, 2003
"... Turbulence in fluids is commonly observed to coexist with relatively large spatial and temporal scale coherent jets. These jets may be steady, vacillate with a definite period, or be irregular. A comprehensive theory for this phenomenon is presented based on the mutual interaction between the coh ..."
Abstract

Cited by 17 (5 self)
 Add to MetaCart
Turbulence in fluids is commonly observed to coexist with relatively large spatial and temporal scale coherent jets. These jets may be steady, vacillate with a definite period, or be irregular. A comprehensive theory for this phenomenon is presented based on the mutual interaction between the coherent jet and the turbulent eddies. When a su#cient number of statistically independent realizations of the eddy field participate in organizing the jet a simplified asymptotic dynamics emerges with progression, as an order parameter such as the eddy forcing is increased, from a stable fixed point associated with a steady symmetric zonal jet through a pitchfork bifurcation to a stable asymmetric jet followed by a Hopf bifurcation to a stable limit cycle associated with a regularly vacillating jet and finally a transition to chaos. This underlying asymptotic dynamics emerges when a su#cient number of ensemble members is retained in the stochastic forcing of the jet but qualitative di#erent mean jet dynamics is found when a small number of ensemble members is retained as is appropriate for many physical systems. Example applications of this theory are presented including a model of midlatitude jet vacillation, emergence and maintenance of multiple jets in turbulent flow, a model of rapid reorganization of storm tracks as a threshold in radiative forcing is passed, and a model of the quasibiennial oscillation. Because the statistically coupled wave/mean flow system discussed is generally globally stable this system also forms the basis for a comprehensive theory for equilibration of unstable jets in turbulent shear flow.