CDC2000 Subspace Identification Methods

Subspace Identification Methods
Home Full List of Titles 1: Proceedings of CDC2000 Discrete Event Systems Control in Communication Systems Optimal Control and Applications I Optimisation Approaches and Methods Model Predictive Control Advances in Linear Estimation Stochastic and Uncertain Systems Nonlinear Control and Applications Nonlinear Estimation and Filtering Formation Control and its Applications New Approaches to Fuzzy Control Manufacturing Systems Automotive Applications Stability Issues in Hybrid Control Recent Advances in Stochastic Networks Optimal Control and Applications II Robust Controller Design - mu, L1 and H2 Constrained and Receding Horizon Control Identification and Control around the World Markov Decision Processes Nonlinear Optimisation Observers for Nonlinear Systems Motion Planning Neural / Fuzzy Stability and Control Motor Control Control of Quantum Phenomena I Hybrid Systems Methods Control in Communication Networks Robustness and Optimisation Bumpless Transfer, Antiwindup and Saturation 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Control Integrated Control and CPU Scheduling Linear Design Techniques Adaptive Disturbance / Noise Compensation Nonlinear Model Predictive Control Sensitivity Design, Analysis and Limitations Analysis of Linear Systems Linear Matrix Inequalities in Design Lyapunov's 2nd Method Robotics: Tracking Control Lagrangian and Hamiltonian Theory Variable Structure Control Machine Vision Signal Processing Methods in Control Applied Nonlinear Control Author Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z	Probing Inputs For Subspace Identification Authors: Alessandro Chiuso, Giorgio Picci, Volume: 1, Page 1544 Paper number 201 Abstract: There is experimental evidence that the standard subspace methods (e.g. the N4SID method) perform poorly in certain conditions where the past signals (past inputs and past outputs) and future input spaces are nearly parallel. Based on an elementary numerical conditioning analysis, this paper describes a class of (system-dependent) input signals (called probing inputs) which lead to the worst possible conditioning of the identification problem. Numerical results are included demonstrating how these input signals may lead to a substantial deterioration of performance of the algorithms in some experimental conditions. CD000201.PDF (From Author) TOP Convergence Rates For Eigenstructure Identification Using Subspace Methods Authors: Albert Benveniste, Michèle Basseville, Laurent Mével, Volume: 1, Page 1550 Paper number 202 Abstract: We apply the general results of companion paper INV0401 in session WeM06-1 on the relationship between identification and local tests, to the estimation of convergence rates for MIMO system eigenstructure identification using subspace algorithms. We provide a new and practical estimator for such convergence rates. CD000202.PDF (From Author) TOP Imposing Stability in Subspace Identification by Regularization Authors: Tony van Gestel, Johan A.K. Suykens, Paul van Dooren, Bart de Moor, Volume: 1, Page 1555 Paper number 203 Abstract: In subspace methods for linear system identification, the system matrices are usually estimated by least squares, based on estimated Kalman filter state sequences and the observed inputs and outputs. For an infinite number of data points and a correct choice of the system order, this least squares estimate of the system matrices is unbiased. However, when using subspace identification on a finite number of data points, the estimated model can become unstable, for a given deterministic system which is known to be stable. In this paper, stability of the estimated model is imposed by adding a regularization term to the least squares cost function. The regularization term used here is the trace of a matrix which involves the dynamical system matrix and a positive (semi-)definite weighting matrix. The amount of regularization needed can be determined by solving a generalized eigenvalue problem. It is shown that the so-called data augmentation method proposed by Chui and Maciejowski corresponds to adding regularization terms with specific choices for the weighting matrix. CD000203.PDF (From Author) TOP Subspace Angles Between Linear Stochastic Models Authors: Katrien de Cock, Bart de Moor, Volume: 1, Page 1561 Paper number 204 Abstract: In this paper we define a notion of principal angles between two linear autoregressive (AR) models by considering the principal angles between the ranges of their infinite observability matrices. We show how a recently defined metric for these models, which is based on their cepstra, is related to the subspace angles between them. The definition of subspace angles is also extended to the linear autoregressive-moving-average (ARMA) model class. CD000204.PDF (From Author) TOP Identification of Multivariable Linear Parameter-Varying Systems Based on Subspace Techniques Authors: Vincent Verdult, Michel Verhaegen, Volume: 1, Page 1567 Paper number 205 Abstract: The paper presents a subspace type of identification method for multivariable linear parameter-varying systems in state space representation with affine parameter dependence. It is shown that a major problem with subspace methods for this kind of systems is the enormous dimensions of the data matrices involved. To overcome the curse of dimensionality, we suggest to use only the most dominant rows of the data matrices in estimating the model. An efficient selection algorithm is discussed that does not require the formation of the complete data matrices, but can process them row by row. CD000205.PDF (From Author) TOP An Improved Subspace Identification Method For Bilinear Systems Authors: Huixin Chen, Jan M. Maciejowski, Volume: 1, Page 1573 Paper number 206 Abstract: Several subspace algorithms for the identification of bilinear systems have been proposed recently. A key practical problem with all of these is the very large size of the data-based matrices which must be constructed in order to `linearise' the problem and allow parameter estimation essentially by regression. Favoreel et al (ACC 1997) proposed an algorithm which gave unbiased results only if the measured input signal was white. Favoreel and De Moor (MTNS 1998) suggested an alternative algorithm for general input signals, but which gave biased estimates. Chen and Maciejowski proposed algorithms for the deterministic (ACC 2000) and deterministic-stochastic (SYSID 2000) cases which give asymptotically unbiased estimates with general inputs, and for which the rate of reduction of bias can be estimated. The computational complexity of these algorithms was also significantly lower than the earlier ones, both because the matrix dimensions were smaller, and because convergence to correct estimates (with sample size) appears to be much faster. In this paper we reduce the matrix dimensions further, by making different choices of subspaces for the decomposition of input-output data. In fact we propose two algorithms: an unbiased one for the case m>=n (m: number of outputs, n:number of states), and an asymptotically unbiased one for the case m CD000206.PDF (From Author) TOP