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179
Dynamic Textures
, 2002
"... Dynamic textures are sequences of images of moving scenes that exhibit certain stationarity properties in time; these include seawaves, smoke, foliage, whirlwind etc. We present a novel characterization of dynamic textures that poses the problems of modeling, learning, recognizing and synthesizing ..."
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Cited by 285 (15 self)
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Dynamic textures are sequences of images of moving scenes that exhibit certain stationarity properties in time; these include seawaves, smoke, foliage, whirlwind etc. We present a novel characterization of dynamic textures that poses the problems of modeling, learning, recognizing and synthesizing dynamic textures on a firm analytical footing. We borrow tools from system identification to capture the "essence" of dynamic textures; we do so by learning (i.e. identifying) models that are optimal in the sense of maximum likelihood or minimum prediction error variance. For the special case of secondorder stationary processes, we identify the model suboptimally in closedform. Once learned, a model has predictive power and can be used for extrapolating synthetic sequences to infinite length with negligible computational cost. We present experimental evidence that, within our framework, even lowdimensional models can capture very complex visual phenomena.
A survey of industrial model predictive control technology
, 2003
"... This paper provides an overview of commercially available model predictive control (MPC) technology, both linear and nonlinear, based primarily on data provided by MPC vendors. A brief history of industrial MPC technology is presented first, followed by results of our vendor survey of MPC control an ..."
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Cited by 199 (5 self)
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This paper provides an overview of commercially available model predictive control (MPC) technology, both linear and nonlinear, based primarily on data provided by MPC vendors. A brief history of industrial MPC technology is presented first, followed by results of our vendor survey of MPC control and identification technology. A general MPC control algorithm is presented, and approaches taken by each vendor for the different aspects of the calculation are described. Identification technology is reviewed to determine similarities and differences between the various approaches. MPC applications performed by each vendor are summarized by application area. The final section presents a vision of the next generation of MPC technology, with an emphasis on potential business and research opportunities.
Flatness and defect of nonlinear systems: Introductory theory and examples
 International Journal of Control
, 1995
"... We introduce flat systems, which are equivalent to linear ones via a special type of feedback called endogenous. Their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of Kalman’s controllability. The distance to flatness is ..."
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Cited by 173 (15 self)
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We introduce flat systems, which are equivalent to linear ones via a special type of feedback called endogenous. Their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of Kalman’s controllability. The distance to flatness is measured by a nonnegative integer, the defect. We utilize differential algebra which suits well to the fact that, in accordance with Willems ’ standpoint, flatness and defect are best defined without distinguishing between input, state, output and other variables. Many realistic classes of examples are flat. We treat two popular ones: the crane and the car with n trailers, the motion planning of which is obtained via elementary properties of planar curves. The three nonflat examples, the simple, double and variable length pendulums, are borrowed from nonlinear physics. A high frequency control strategy is proposed such that the averaged systems become flat. ∗This work was partially supported by the G.R. “Automatique ” of the CNRS and by the D.R.E.D. of the “Ministère de l’Éducation Nationale”. 1 1
N4SID: Subspace Algorithms for the Identification of Combined DeterministicStochastic Systems
, 1994
"... Recently a great deal of attention has been given to numerical algorithms for subspace state space system identification (N4SID). In this paper, we derive two new N4SID algorithms to identify mixed deterministicstochastic systems. Both algorithms determine state sequences through the projection of ..."
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Cited by 102 (12 self)
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Recently a great deal of attention has been given to numerical algorithms for subspace state space system identification (N4SID). In this paper, we derive two new N4SID algorithms to identify mixed deterministicstochastic systems. Both algorithms determine state sequences through the projection of input and output data. These state sequences are shown to be outputs of nonsteady state Kalman filter banks. From these it is easy to determine the state space system matrices. The N4SID algorithms are always convergent (noniterative) and numerically stable since they only make use of QR and Singular Value Decompositions. Both N4SID algorithms are similar, but the second one trades off accuracy for simplicity. These new algorithms are compared with existing subspace algorithms in theory and in practice. Key words : Subspace identification, nonsteady state Kalman filter, Riccati difference equations, QR and Singular Value Decomposition 1 Introduction The greater part of the systems ide...
Complementarity Modeling of Hybrid Systems
, 1998
"... A complementarity framework is described for the modeling of certain classes of mixed continuous /discrete dynamical systems. The use of such a framework is wellknown for mechanical systems with inequality constraints, but we give a more general formulation which applies for instance also to sys ..."
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Cited by 50 (11 self)
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A complementarity framework is described for the modeling of certain classes of mixed continuous /discrete dynamical systems. The use of such a framework is wellknown for mechanical systems with inequality constraints, but we give a more general formulation which applies for instance also to systems with relays in a feedback loop. The main theoretical results in the paper are concerned with uniqueness of smooth continuations; the solution of this problem requires the construction of a map from the continuous state to the discrete state. A crucial technical tool is the socalled linear complementarity problem (LCP); we introduce various generalizations of this problem. Specific results are obtained for Hamiltonian systems, passive systems, and linear systems.
The Behavior of Convolutional Codes
, 1995
"... It is well known that a convolutional code can be viewed as a linear system over a finite field. In this paper we develop this viewpoint for convolutional codes using several recent innovations from the systems theory literature. In particular we define codes as behaviors of a set of compact support ..."
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Cited by 47 (16 self)
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It is well known that a convolutional code can be viewed as a linear system over a finite field. In this paper we develop this viewpoint for convolutional codes using several recent innovations from the systems theory literature. In particular we define codes as behaviors of a set of compact support time trajectories over a vector space. We also consider several different representations of codes, in particular generalized first order representations. As an application of these ideas, we present a BCH construction technique for convolutional codes that yields optimal high rate codes.
On The Complexity Of Computing Determinants
 COMPUTATIONAL COMPLEXITY
, 2001
"... We present new baby steps/giant steps algorithms of asymptotically fast running time for dense matrix problems. Our algorithms compute the determinant, characteristic polynomial, Frobenius normal form and Smith normal form of a dense n n matrix A with integer entries in (n and (n bi ..."
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Cited by 45 (17 self)
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We present new baby steps/giant steps algorithms of asymptotically fast running time for dense matrix problems. Our algorithms compute the determinant, characteristic polynomial, Frobenius normal form and Smith normal form of a dense n n matrix A with integer entries in (n and (n bit operations; here denotes the largest entry in absolute value and the exponent adjustment by "+o(1)" captures additional factors for positive real constants C 1 , C 2 , C 3 . The bit complexity (n results from using the classical cubic matrix multiplication algorithm. Our algorithms are randomized, and we can certify that the output is the determinant of A in a Las Vegas fashion. The second category of problems deals with the setting where the matrix A has elements from an abstract commutative ring, that is, when no divisions in the domain of entries are possible. We present algorithms that deterministically compute the determinant, characteristic polynomial and adjoint of A with n and O(n ) ring additions, subtractions and multiplications.
On the complexity of polynomial matrix computations
 Proceedings of the 2003 International Symposium on Symbolic and Algebraic Computation
, 2003
"... ..."
Optimal and Robust Control and Estimation of Linear Paths to Transition
 J. Fluid Mech
, 1998
"... this paper is not valid. Iterative optimal control approaches over finite time intervals, which make use of full state information, may still be formulated (Abergel & Temam 1990) and performed (Moin & Bewley 1995) with impressive results. In order to make such schemes practical, one must understand ..."
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Cited by 31 (9 self)
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this paper is not valid. Iterative optimal control approaches over finite time intervals, which make use of full state information, may still be formulated (Abergel & Temam 1990) and performed (Moin & Bewley 1995) with impressive results. In order to make such schemes practical, one must understand how to account for disturbances in a rigorous fashion and how to estimate accurately the necessary components of the state (for instance, the location and strength of the nearwall coherent structures) based on limited flow measurements. The present paper makes these concepts clear in a fluidmechanical sense, albeit for a linear problem, and thus provides a step in this development. Techniques to extend the robust control concept, introduced for problems in fluid mechanics in the present work, to nonlinear problems (such as turbulence) are discussed in Bewley, Moin & Temam (1997) and Bewley, Temam & Ziane (1998). 1.1. Outline of paper The structure of the remainder of the paper is: Section 2: the governing equations for the flow stability problem are put in a standard notation which makes subsequent application of control theory straightforward. Two specific cases are identified to be examined in detail: one supercritical and one subcritical. Section 3: the control approach and numerical method used are briefly summarized. Section 4: the methods used to analyse the openloop and closedloop systems are reviewed. Section 5: the uncontrolled (`openloop') systems are studied in detail. Section 6: the controlled (`closedloop') systems are studied in detail. Root loci, which demonstrate the movement of the closedloop system eigenvalues with respect to control parameters, are shown to illuminate some general trends, but fail to provide a quantitative measure of system performa...