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ABSTRACT: The minimum-time control problem consists in finding a control policy that
will drive a given dynamic system from a given initial state to a given target
state (or a set of states) as quickly as possible. This is a well-known
challenging problem in optimal control theory for which closed-form solutions
exist only for a few systems of small dimensions. This paper presents a very
generic solution to the minimum-time problem for arbitrary discrete-time linear
systems. It is a numerical solution based on sparse optimization, that is the
minimization of the number of nonzero elements in the state sequence over a
fixed control horizon. We consider both single input and multiple inputs
systems. An important observation is that, contrary to the continuous-time
case, the minimum-time control for discrete-time systems is not necessarily
entirely bang-bang.
09/2011;
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Proceedings of the 49th IEEE Conference on Decision and Control, CDC 2010, December 15-17, 2010, Atlanta, Georgia, USA; 01/2010
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ICINCO 2009, Proceedings of the 6th International Conference on Informatics in Control, Automation and Robotics, Volume Robotics and Automation, Milan, Italy, July 2-5, 2009; 01/2009
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IFAC Symposium on System Identification 2009; 01/2009
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ABSTRACT: In this paper we present an online recursive clustering algorithm based on incremental and decremental Support Vector Machine
(SVM). Developed to learn evolving clusters from non-stationary data, it is able to achieve an efficient multi-class clustering
in a non-stationary environment. With a new similarity measure and different procedures (Creation, Adaptation: incremental
and decremental learning, Fusion and Elimination) this classifier can provide optimal updated models of data.
09/2008: pages 336-345;
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ABSTRACT: This paper presents a new online clustering algorithm called SAKM (Self-Adaptive Kernel Machine) which is developed to learn continuously evolving clusters from non-stationary data. Based on SVM and kernel methods, the SAKM algorithm uses a fast adaptive learning procedure to take into account variations over time. Dedicated to online clustering in a multi-class environment, the algorithm designs an unsupervised neural architecture with self-adaptive abilities. Based on a specific kernel-induced similarity measure, the SAKM learning procedures consist of four main stages: Creation, Adaptation, Fusion and Elimination. In addition to these properties, the SAKM algorithm is attractive to be computationally efficient in online learning of real-drifting targets. After a theoretical study of the error convergence bound of the SAKM local learning, a comparison with NORMA and ALMA algorithms is made. In the end, some experiments conducted on simulation data, UCI benchmarks and real data are given to illustrate the capacities of the SAKM algorithm for online clustering in non-stationary and multi-class environment.
Neural Networks 07/2008; 21(9):1287-301. · 2.18 Impact Factor
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ABSTRACT: This paper is concerned with the identification of piecewise linear MIMO state space systems in a recursive way. The proposed method summons up benefits of recursive parameters estimation, on-line switching times detection and on-line order estimation. A structured identification scheme which applied on-line, allows to track both the extended ob-servability matrix range space and its dimension. This method is used on-line to blindly identify switching systems and to label the different submodels. Since subspace identification methods rely on batch data block matrices, a minimum dwell time in each discrete state is necessary to achieve good performances. Simulation results comfort this point and illustrate the abilities and the benefits of the proposed approach.
European Control Conference 2007; 01/2007
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ABSTRACT: This paper presents a recursive scheme for the identification of Ham-merstein MIMO models. The Markov parameters of the system are determined first by a Least Squares Support Vector Machines (LS-SVM) regression through an over-parameterization technique. Then, a state space realization of the system is retrieved using an adapted online subspace identification method. Simulation results are provided to demonstrate the effectiveness of the algorithm in the presence of white output noise.
IFAC Workshop Adaptive and Learning Control and Signal Processing 2007; 01/2007
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ABSTRACT: The problem of the recursive identification of MIMO state space models in the framework of subspace methods is considered in this article. Two new algorithms, based on a recursive formulation of the MOESP identification class, are developed. The specific feature of these methods is that they share a single algorithm to recursively estimate a basis of the observability matrix. Two propagator based (Munier and Delisle, 1991) criteria are introduced. A sequential RLS algorithm is proposed to equally minimise these cost functions. The benefits of these new techniques in comparison with EIVPAST and UDPAST (Lovera et al., 2000) are emphasized with a simulation example.
IFAC World Congress, Praha, Czech Republic; 07/2005
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ABSTRACT: The problem of the recursive identification of MIMO state space models in the framework of subspace methods is considered in this article. Two new algorithms, based on a recursive formulation of the MOESP identification class, are developed. The specific feature of these methods is that they share a single algorithm to recursively estimate a basis of the observability matrix. Two propagator based (Munier and Delisle, 1991) criteria are introduced. A sequential RLS algorithm is proposed to equally minimise these cost functions. The benefits of these new techniques in comparison with EIVPAST and UDPAST (Lovera et al., 2000) are emphasized with a simulation example.
IFAC World Congress 2005; 01/2005
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Artificial Neural Networks: Formal Models and Their Applications - ICANN 2005, 15th International Conference, Warsaw, Poland, September 11-15, 2005, Proceedings, Part II; 01/2005
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IASTED International Conference on Artificial Intelligence and Applications, part of the 23rd Multi-Conference on Applied Informatics, Innsbruck, Austria, February 14-16, 2005; 01/2005
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ABSTRACT: In the context of evolutionary data classification, dynamical modeling techniques are useful to continuously learn clusters
models. Dedicated to on-line clustering, the AUDyC (Auto-adaptive and Dynamical Clustering) algorithm is an unsupervised neural
network with auto-adaptive abilities in nonstationary environment. These particular abilities are based on specific learning
rules that are developed into three stages: “Classification”, “Evaluation” and “Fusion”. In this paper, we propose a new densities
merge mechanism to improve the “Fusion” stage in order to avoid some local optima drawbacks of Gaussian fitting. The novelty
of our approach is to use an ambiguity rule of fuzzy modelling with new merge acceptance criteria. Our approach can be generalized
to any type of fuzzy classification method using Gaussian models. Some experiments are presented to show the efficiency of
our approach to circumvent to AUDyC NN local optima problems.
12/2004: pages 155-158;
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ABSTRACT: In this article, a new recursive identification method based on subspace algo-rithms is proposed. This method is directly inspired by the Propagator Method used in sensor array signal processing to estimate directions of arrival (DOA) of waves impinging an antenna array. Particularly, a new quadratic criterion and a recursive formulation of the estimation of the subspace spanned by the observability matrix are presented. The problem of process and measurement noises is solved by introducing an instrumental variable within the minimized criterion.
IFAC Symposium on System Identification 2003; 01/2003
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ABSTRACT: In this work, a recursive procedure is derived for the identification of switched affine models from input-output data. Starting from some initial values of the parameter vectors that represent the different submodels, the proposed algorithm alternates between data assignment to submodels and parameter update. At each time instant, the discrete state is determined as the index of the submodel that, in term of the prediction error, appears to have most likely generated the regressor vector observed at that instant. Given the estimated discrete state, the associated parameter vector is updated based on recursive least squares. Convergence of the whole procedure although not theoretically proved, seems to be easily achieved when enough rich data are available. Finally performance is tested through some computer simulations and the modeling of an open channel system.
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ABSTRACT: We consider the problem of identifying switched linear state space models from a finite set of input-output data. This is a challenging problem, which requires inferring both the discrete state and the parameter matrices associated with each discrete state. An important contribution of our work is that we do not make the restrictive assumption of minimum dwell time between the switches, as it is customary in methods that deal with such models. We first propose a technique for eliminating the unknown continuous state from the model equations under an appropriate assumption of observability. On a time horizon, this gives us a new switched input-output relation that involves structured intermediary matrices, which depend on the state space representation matrices. To estimate the intermediary matrices, we present a randomly initialized algorithm that alternates between data classification and parameter update via recursive least squares. Given these matrices, the parameters associated to the different discrete states can be computed after a correct estimation of the discrete state.
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ABSTRACT: In this paper, we propose a new method for the identification of linear Multiple Inputs-Multiple Outputs (MIMO) systems. By introducing a particular user-defined matrix that does not change the rank of the extended observability matrix when multiplying this latter matrix on the left, the subspace identification problem is recasted into a simple least squares problem with all regressors available. Therefore, the Singular Value Decomposition algorithm which is a customary tool in subspace identification can be avoided, thus making our method appealing for recursive implementation. The technique is such that the state coordinates basis of the estimated matrices is completely determined by the aforementioned user-defined matrix, that is, given such a matrix, the state basis of the identified matrices does not change with respect to the realization of input-output data.
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ABSTRACT: In this work, a recursive procedure is derived for the identification of switched linear models from input–output data. Starting from some initial values of the parameter vectors that represent the different submodels, the proposed algorithm alternates between data assignment to submodels and parameter update. At each time instant, the discrete state is determined as the index of the submodel that, in terms of the prediction error (or the posterior error), appears to have most likely generated the regressor vector observed at that instant. Given the estimated discrete state, the associated parameter vector is updated based on recursive least squares or any fast adaptive linear identifier. Convergence of the whole procedure although not theoretically proved, seems to be easily achieved when enough rich data are available. It has been also observed that by appropriately choosing the data assignment criterion, the proposed on-line method can be extended to deal also with the identification of piecewise affine models. Finally, performance is tested through some computer simulations and the modeling of an open channel system.
Nonlinear Analysis Hybrid Systems 5(2):242-253.
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ABSTRACT: Cette communication concerne l'identification de systèmes linéaires à commutations. Ce problème, particulièrement délicat à cause du couplage entre l'état discret et l'état continu est traité de façon récursive via une alternance entre la classification des données de régression et l'estimation des paramètres des sous-modèles. La méthode proposée, sans être moins performante, présente un coût calculatoire réduit par rapport aux méthodes existantes. De plus, son caractère récursif lui permet de surmonter, moyennant une bonne initialisation, de légères variations de paramètres, inévitables dans un processus réel. Une comparaison avec une approche bayésienne récemment proposée dans la littérature démontre l'avantage de notre méthode.
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ABSTRACT: Cet article, en lien avec la surveillance de systèmes non-stationnaires, présente une nouvelle approche de suivi basée sur la reconnaissance de formes. Le principe retenu consiste à coupler un algorithme d’identification récursive à une technique de classification dynamique. Dans un premier temps, la technique d’identification en ligne est décrite. Cette estimation récursive d’un modèle linéaire permet d’extraire un vecteur caractéristique de l’état de fonctionnement du procédé. Dans un second temps, ce vecteur est utilisé par un algorithme de classification pour déterminer le mode de fonctionnement courant. Ses capacités à adapter en continu la modélisation de l’espace de décision (modes connus) et à suivre ses évolutions sont brièvement détaillées. Des résultats issus d’exemples de simulation sont finalement proposés.
