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225
Perspectives on system identification
- In Plenary talk at the proceedings of the 17th IFAC World Congress, Seoul, South Korea
, 2008
"... System identification is the art and science of building mathematical models of dynamic systems from observed input-output data. It can be seen as the interface between the real world of applications and the mathematical world of control theory and model abstractions. As such, it is an ubiquitous ne ..."
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Cited by 167 (3 self)
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System identification is the art and science of building mathematical models of dynamic systems from observed input-output data. It can be seen as the interface between the real world of applications and the mathematical world of control theory and model abstractions. As such, it is an ubiquitous necessity for successful applications. System identification is a very large topic, with different techniques that depend on the character of the models to be estimated: linear, nonlinear, hybrid, nonparametric etc. At the same time, the area can be characterized by a small number of leading principles, e.g. to look for sustainable descriptions by proper decisions in the triangle of model complexity, information contents in the data, and effective validation. The area has many facets and there are many approaches and methods. A tutorial or a survey in a few pages is not quite possible. Instead, this presentation aims at giving an overview of the “science ” side, i.e. basic principles and results and at pointing to open problem areas in the practical, “art”, side of how to approach and solve a real problem. 1.
Identification of piecewise affine systems via mixed-integer programming
- AUTOMATICA
, 2004
"... This paper addresses the problem of identification of hybrid dynamical systems, by focusing the attention on hinging hyperplanes (HHARX) and Wiener piecewise affine (W-PWARX) autoregressive exogenous models. In particular, we provide algorithms based on mixed-integer linear or quadratic programming ..."
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Cited by 52 (5 self)
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This paper addresses the problem of identification of hybrid dynamical systems, by focusing the attention on hinging hyperplanes (HHARX) and Wiener piecewise affine (W-PWARX) autoregressive exogenous models. In particular, we provide algorithms based on mixed-integer linear or quadratic programming which are guaranteed to converge to a global optimum. For the special case where switches occur only seldom in the estimation data, we also suggest a way of trading off between optimality and complexity by using a change detection approach.
Online prediction of time series data with kernels
- IEEE TRANS. SIGNAL PROCESSING
, 2009
"... Kernel-based algorithms have been a topic of considerable interest in the machine learning community over the last ten years. Their attractiveness resides in their elegant treatment of nonlinear problems. They have been successfully applied to pattern recognition, regression and density estimation. ..."
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Cited by 50 (20 self)
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Kernel-based algorithms have been a topic of considerable interest in the machine learning community over the last ten years. Their attractiveness resides in their elegant treatment of nonlinear problems. They have been successfully applied to pattern recognition, regression and density estimation. A common characteristic of kernel-based methods is that they deal with kernel expansions whose number of terms equals the number of input data, making them unsuitable for online applications. Recently, several solutions have been proposed to circumvent this computational burden in time series prediction problems. Nevertheless, most of them require excessively elaborate and costly operations. In this paper, we investigate a new model reduction criterion that makes computationally demanding sparsification procedures unnecessary. The increase in the number of variables is controlled by the coherence parameter, a fundamental quantity that characterizes the behavior of dictionaries in sparse approximation problems. We incorporate the coherence criterion into a new kernel-based affine projection algorithm for time series prediction. We also derive the kernel-based normalized LMS algorithm as a particular case. Finally, experiments are conducted to compare our approach to existing methods.
A boundederror approach to piecewise affine system identification
- IEEE Transactions on Automatic Control
, 2005
"... Abstract — This paper proposes a three-stage procedure for ..."
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Cited by 48 (1 self)
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Abstract — This paper proposes a three-stage procedure for
Nonlinear Black-Box Models in System Identification: Mathematical Foundations
, 1995
"... In this paper we discuss several aspects of the mathematical foundations of non-linear black-box identification problem. As we shall see that the quality of the identification procedure is always a result of a certain trade-off between the expressive power of the model we try to identify (the larger ..."
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Cited by 47 (6 self)
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In this paper we discuss several aspects of the mathematical foundations of non-linear black-box identification problem. As we shall see that the quality of the identification procedure is always a result of a certain trade-off between the expressive power of the model we try to identify (the larger is the number of parameters used to describe the model, more flexible would be the approximation), and the stochastic error (which is proportional to the number of parameters). A consequence of this trade-off is a simple fact that good approximation technique can be a basis of good identification algorithm. From this point of view we consider different approximation methods, and pay special attention to spatially adaptive approximants. We introduce wavelet and "neuron" approximations and show that they are spatially adaptive. Then we apply the acquired approximation experience to estimation problems. Finally, we consider some implications of these theoretic developments for the practically...
On-Board Component Fault Detection and Isolation Using the Statistical Local Approach
, 1997
"... We describe both the key principles and real application examples of a unified theory which allows us to perform the on-board incipient fault detection and isolation tasks involved in monitoring for condition-based maintenance. We stress that, when designing detection algorithms, the main conceptual ..."
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Cited by 41 (6 self)
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We describe both the key principles and real application examples of a unified theory which allows us to perform the on-board incipient fault detection and isolation tasks involved in monitoring for condition-based maintenance. We stress that, when designing detection algorithms, the main conceptual task is to select a convenient estimating function. ml, ls, iv and subspace identification methods are addressed in this perspective.
Recurrent Least Squares Support Vector Machines
- IEEE Transactions on Circuits and Systems-I
, 2000
"... The method of support vector machines has been developed for solving classication and static function approximation problems. In this paper we introduce support vector machines within the context of recurrent neural networks. Instead of Vapnik's epsilon insensitive loss function, we consider a ..."
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Cited by 30 (8 self)
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The method of support vector machines has been developed for solving classication and static function approximation problems. In this paper we introduce support vector machines within the context of recurrent neural networks. Instead of Vapnik's epsilon insensitive loss function, we consider a least squares version related to a cost function with equality constraints for a recurrent network. Essential features of support vector machines remain such as Mercer's condition and the fact that the output weights are a Lagrange multiplier weighted sum of the data points. The solution to recurrent least squares support vector machines is characterized by a set of nonlinear equations. Due to its high computational complexity, we focus on a limit case of assigning the squared error an innitely large penalty factor with early stopping as a form of regularization. The eectiveness of the approach is demonstrated on trajectory learning of the double scroll attractor in Chua's circuit. Keywords. Recurrent neural networks, Support vector machines, Radial basis functions, Double scroll. 1
A Taxonomy for Spatiotemporal Connectionist Networks Revisited: The Unsupervised Case
- Neural Computation
, 2003
"... Spatiotemporal connectionist networks (STCN's) comprise an important class of neural models that can deal with patterns distributed both in time and space. In this paper, we widen the application domain of the taxonomy for supervised STCN's recently proposed by Kremer (2001) to the unsuper ..."
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Cited by 27 (1 self)
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Spatiotemporal connectionist networks (STCN's) comprise an important class of neural models that can deal with patterns distributed both in time and space. In this paper, we widen the application domain of the taxonomy for supervised STCN's recently proposed by Kremer (2001) to the unsupervised case. This is possible through a reinterpretation of the state vector as a vector of latent (hidden) variables, as proposed by Meinicke (2000). The goal of this generalized taxonomy is then to provide a nonlinear generative framework for describing unsupervised spatiotemporal networks, making it easier to compare and contrast their representational and operational characteristics. Computational properties, representational issues and learning are also discussed and a number of references to the relevant source publications are provided. It is argued that the proposed approach is simple and more powerful than the previous attempts, from a descriptive and predictive viewpoint. We also discuss the relation of this taxonomy with automata theory and state space modeling, and suggest directions for further work.
Just-in-Time Models with Applications to Dynamical Systems
- Dept. of EE, LinkOping University. S-581 83 LinkOping
, 1997
"... System identification deals with the problem of estimating models of dynamical systems given observations from the systems. In this thesis we focus on the nonlinear modeling problem, and, in particular, on the situation that occurs when a very large amount of data is available. Traditional treatmen ..."
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Cited by 26 (3 self)
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System identification deals with the problem of estimating models of dynamical systems given observations from the systems. In this thesis we focus on the nonlinear modeling problem, and, in particular, on the situation that occurs when a very large amount of data is available. Traditional treatments of the estimation problem in statistics and system identification have mainly focused on global modeling approaches, i.e., the model has been optimized using the entire data set. However, when the number of samples becomes large, this approach becomes less attractive mainly because of the computational complexity. We instead assume that all observations are stored in a database, and that models are built dynamically as the actual need arises. When a model is really needed in a neighborhood around an operating point, a subset of the data closest to the operating point is retrieved from the database, and a local modeling operation is performed on that subset. For this concept, the name Jus...
Approximating networks and extended Ritz method for the solution of functional optimization problems
- J. Optim. Theory Appl
"... Abstract. Functional optimization problems can be solved analytically only if special assumptions are verified; otherwise, approximations are needed. The approximate method that we propose is based on two steps. First, the decision functions are constrained to take on the structure of linear combina ..."
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Cited by 24 (16 self)
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Abstract. Functional optimization problems can be solved analytically only if special assumptions are verified; otherwise, approximations are needed. The approximate method that we propose is based on two steps. First, the decision functions are constrained to take on the structure of linear combinations of basis functions containing free parameters to be optimized (hence, this step can be considered as an extension to the Ritz method, for which fixed basis functions are used). Then, the functional optimization problem can be approximated by nonlinear programming problems. Linear combinations of basis functions are called approximating networks when they benefit from suitable density properties. We term such networks nonlinear (linear) approximating networks if their basis functions contain (do not contain) free parameters. For certain classes of d-variable functions to be approximated, nonlinear approximating networks may require a number of parameters increasing moderately with d, whereas linear approximating networks may be ruled out by the curse of dimensionality. Since the cost functions of the resulting nonlinear programming problems include complex averaging operations, we minimize such functions by stochastic approximation algorithms. As important special cases, we consider stochastic optimal control and estimation problems. Numerical examples show the effectiveness of the method in solving optimization problems stated in 1
