Results 1  10
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27
Robust identification of switched affine systems via momentsbased convex optimization
 In Proc. 48th IEEE Conf. Dec. Control
, 2009
"... Abstract — This paper addresses the problem of robust identification of a class of discretetime affine hybrid systems, switched affine models, in a set membership framework. Given a finite collection of noisy input/output data and a bound on the number of subsystems, the objective is to identify a ..."
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Cited by 10 (8 self)
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Abstract — This paper addresses the problem of robust identification of a class of discretetime affine hybrid systems, switched affine models, in a set membership framework. Given a finite collection of noisy input/output data and a bound on the number of subsystems, the objective is to identify a suitable set of affine models along with a switching sequence that can explain the available experimental information. Our method builds upon an algebraic procedure proposed by Vidal et al. for noise free measurements. In the presence of norm bounded noise, this algebraic procedure leads to a very challenging nonconvex polynomial optimization problem. Our main result shows that this problem can be reduced to minimizing the rank of a matrix whose entries are affine in the optimization variables, subject to a convex constraint imposing that these variables are the moments of an (unknown) probability distribution function with finite support. Appealing to well known convex relaxations of rank leads to an overall semidefinite optimization problem that can be efficiently solved. These results are illustrated with two examples showing substantially improved identification performance in the presence of noise. I.
Hybrid system identification via sparse polynomial optimization
 In American Control Conference
, 2010
"... AbstractIn this paper, the problem of identifying discrete time affine hybrid systems with measurement noise is considered. Given a finite collection of measurements and a bound on the noise, the objective is to identify a hybrid system with the smallest number of subsystems that is compatible wi ..."
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Cited by 5 (4 self)
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AbstractIn this paper, the problem of identifying discrete time affine hybrid systems with measurement noise is considered. Given a finite collection of measurements and a bound on the noise, the objective is to identify a hybrid system with the smallest number of subsystems that is compatible with the a priori information. While this problem has been addressed in the literature if the input/output data is noisefree or corrupted by process noise, it remains open for the case of measurement noise. To handle this case, we propose a new approach based on recasting the problem into a polynomial optimization form and exploiting its inherent sparse structure to obtain computationally tractable problems. Combining these ideas with a randomized Hit and Run type approach leads to further computational complexity reduction, allowing for solving realistically sized problems. Numerical examples are provided, illustrating the effectiveness of the algorithm and its potential to handle large size problems.
Learning Nonlinear Hybrid Systems: from Sparse Optimization to Support Vector Regression
, 2013
"... This paper deals with the identification of hybrid systems switching between nonlinear subsystems of unknown structureand focuseson the connectionswith a family of machine learning algorithms known as support vector machines. In particular, we consider a recent approach to nonlinear hybrid system id ..."
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Cited by 2 (1 self)
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This paper deals with the identification of hybrid systems switching between nonlinear subsystems of unknown structureand focuseson the connectionswith a family of machine learning algorithms known as support vector machines. In particular, we consider a recent approach to nonlinear hybrid system identification based on a convex relaxation of a sparse optimization problem. In this approach, the submodels are iteratively estimated one by one by maximizing the sparsity of the corresponding error vector. We extend this approach in several ways. First, we relax the sparsity condition by introducing robust sparsity, which can be optimized through the minimization of a modified ℓ1norm or, equivalently, of the εinsensitive loss function. Then, we show that, depending on the choice of regularizer, the method is equivalent to different forms of support vector regression. More precisely, thesubmodelscanbeestimatedbyiterativelysolving a classical support vector regression problem, in which the sparsity of support vectors relates to the sparsity of the error vector in the considered hybrid system identification framework. This allows us to extend theoretical results as well as efficient optimization algorithms from the field of machine learning to the hybrid system framework.
Identification of MIMO switched statespace models
 In Proc. of the American Control Conference (ACC
, 2013
"... Abstract — Identifying switched linear models directly from inputoutput measurements only is known to be a nontrivial identification problem. When switched statespace models are considered in a general setting and both the continuous state and the discrete mode are unmeasured, the problem proves ..."
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Cited by 2 (1 self)
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Abstract — Identifying switched linear models directly from inputoutput measurements only is known to be a nontrivial identification problem. When switched statespace models are considered in a general setting and both the continuous state and the discrete mode are unmeasured, the problem proves to be a much harder realization problem. The present paper describes a method for identifying discretetime switched linear statespace models from inputstateoutput measurements. While the discrete mode is unknown, we assume here that the continuous state is measured along with the input and output signals. Given a finite collection of such measured data, we propose a sparsityinducing optimization approach for estimating the matrices associated with each submodel. I.
Hybrid System Identification: An SDP Approach
"... Abstract — The problem of identifying discrete time affine hybrid systems with noisy measurements is addressed in this paper. Given a finite number of measurements of input/output and a bound on the measurement noise, the objective is to identify a switching sequence and a set of affine models that ..."
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Cited by 2 (2 self)
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Abstract — The problem of identifying discrete time affine hybrid systems with noisy measurements is addressed in this paper. Given a finite number of measurements of input/output and a bound on the measurement noise, the objective is to identify a switching sequence and a set of affine models that are compatible with the a priori information, while minimizing the number of affine models. While this problem has been successfully addressed in the literature if the input/output data is noisefree or corrupted by process noise, results for the case of measurement noise are limited, e.g., a randomized algorithm has been proposed in a previous paper [3]. In this paper, we develop a deterministic approach. Namely, by recasting the identification problem as polynomial optimization, we develop deterministic algorithms, in which the inherent sparse structure is exploited. A finite dimensional semidefinite problem is then given which is equivalent to the identification problem. Moreover, to address computational complexity issues, an equivalent rank minimization problem subject to deterministic LMI constraints is provided, as efficient convex relaxations for rank minimization are available in the literature. Numerical examples are provided, illustrating the effectiveness of the algorithms. I.
Convex relaxations for robust identification of hybrid models
, 2010
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Hybrid System Identification with Faulty Measurements and its Application to Activity Analysis
"... Abstract — This paper addresses the problem of set membership identification of a class of discretetime affine hybrid systems, switched affine models, in the presence of sensor failures. Given a finite collection of input/output measurements and a bound on the number of subsystems, the objective is ..."
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Cited by 1 (0 self)
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Abstract — This paper addresses the problem of set membership identification of a class of discretetime affine hybrid systems, switched affine models, in the presence of sensor failures. Given a finite collection of input/output measurements and a bound on the number of subsystems, the objective is to identify a suitable set of affine models along with a switching sequence that can explain the available experimental information. Contrary to existing work, here we allow for instantaneous failures in the measurement sensors at unknown times. These failures lead to corrupted input/output data, that if used in the identification process would result in substantial identification errors. The main result of the paper shows that, exploiting the fact that these failures are infrequent, combined with an algebraicgeometric argument, allows for recasting the problem into an optimization form where the objective is to simultaneously minimize the rank of a matrix and the number of nonzero rows of a second one. While in principle this is a challenging, nonconvex problem, exploiting recent results on convex relaxations of rank and blocksparsity leads to an efficient, semidefinite optimization based identification algorithm. Finally, these results are illustrated using both simulations and a practical example that arises in computer vision where the aim is to analyze the activity of a person in the presence of sensor failures. I.
Model (in)validation of switched arx systems with unknown switches and its application to activity monitoring
 In Proc. 49th IEEE Conf. Dec. Control
, 2010
"... Abstract — Identification of switched linear systems has received considerable attention during the past few years. Since the problem is generically NPHard, the majority of existing algorithms are based on heuristics or relaxations. Therefore, it is crucial to check the validity of the identified m ..."
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Abstract — Identification of switched linear systems has received considerable attention during the past few years. Since the problem is generically NPHard, the majority of existing algorithms are based on heuristics or relaxations. Therefore, it is crucial to check the validity of the identified models against additional experimental data. This paper addresses the problem of model (in)validation for multiinput multioutput switched affine autoregressive exogenous systems with unknown switches. Our main result provides necessary and sufficient conditions for a given model to be (in)validated by the experimental data. In principle, checking these conditions requires solving a sequence of convex optimization problems involving increasingly large matrices. However, as we show in the paper, if in the process of solving these problems either a positive solution is found or the socalled flat extension property holds, then the process terminates with a certificate that either the model has been invalidated or that the experimental data is indeed consistent with the model and a–priori information. By using duality, the proposed approach exploits the inherently sparse structure of the optimization problem to substantially reduce its computational complexity. The effectiveness of the proposed method is illustrated using both academic examples and a nontrivial problem arising in computer vision: activity monitoring. I.
Convex Certificates for Model (In)validation of Switched Affine Systems with Unknown Switches
, 2014
"... Checking validity of a model is a crucial step in the process of system identification. This is especially true when dealing with switched affine systems since, in this case, the problem of system identification from noisy data is known to be generically NPHard and can only be solved in practice by ..."
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Checking validity of a model is a crucial step in the process of system identification. This is especially true when dealing with switched affine systems since, in this case, the problem of system identification from noisy data is known to be generically NPHard and can only be solved in practice by using heuristics and relaxations. Therefore, before the identified models can be used for instance for controller design, they should be systematically validated against additional experimental data. In this paper we address the problem of model (in)validation for multiinput multioutput switched affine systems in output error form with unknown switches. As a first step, we prove that necessary and sufficient invalidation certificates can be obtained by solving a sequence of convex optimization problems. In principle, these problems involve increasingly large matrices. However, as we show in the paper by exploiting recent results from semialgebraic geometry, the proposed algorithm is guaranteed to stop after a finite number of steps that can be be explicitly computed from the apriori information. In addition, this algorithm exploits the sparse structure of the underlying optimization problem to substantially reduce the computational burden. The effectiveness of the proposed method is illustrated using both academic examples and a nontrivial problem arising in computer vision: activity monitoring.
linear
, 2012
"... Estimating the probability of success of a simple algorithm for switched ..."
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