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18
DETERMINANT MAXIMIZATION WITH LINEAR MATRIX INEQUALITY CONSTRAINTS
"... The problem of maximizing the determinant of a matrix subject to linear matrix inequalities arises in many fields, including computational geometry, statistics, system identification, experiment design, and information and communication theory. It can also be considered as a generalization of the s ..."
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Cited by 183 (18 self)
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The problem of maximizing the determinant of a matrix subject to linear matrix inequalities arises in many fields, including computational geometry, statistics, system identification, experiment design, and information and communication theory. It can also be considered as a generalization of the semidefinite programming problem. We give an overview of the applications of the determinant maximization problem, pointing out simple cases where specialized algorithms or analytical solutions are known. We then describe an interiorpoint method, with a simplified analysis of the worstcase complexity and numerical results that indicate that the method is very efficient, both in theory and in practice. Compared to existing specialized algorithms (where they are available), the interiorpoint method will generally be slower; the advantage is that it handles a much wider variety of problems.
... Identification and Model Quality Evaluation
 IEEE Transactions on Automatic Control
, 1997
"... Set membership H1 identification is investigated using timedomain data and mixed parametric and nonparametric models as well as supposing power bounded measurement errors. The problem of optimally estimating the unknown parameters and evaluating the minimal worst case identification error, called r ..."
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Cited by 9 (1 self)
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Set membership H1 identification is investigated using timedomain data and mixed parametric and nonparametric models as well as supposing power bounded measurement errors. The problem of optimally estimating the unknown parameters and evaluating the minimal worst case identification error, called radius of information, is solved. For classes of models affine in the parameters, the radius of information is obtained as function of the H1 norm of the unmodeled dynamics. A method is given for estimating this norm from the available data and some general a priori information on the unmodeled dynamics, thus allowing the actual evaluation of the radius of information. The radius represents a measure of the "predictive ability" of the considered class of models, and it is then used for comparing the quality of different classes of models and for the order selection of their parametric part. The effectiveness of the proposed procedure is tested on some numerical examples and compared with stan...
On comparing statistical and setbased methods in sensor data fusion
 In Proc. IEEE Int. Conf. Robotics and Automation
, 1993
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Visual Data Fusion for Objects Localization by Active Vision
, 2002
"... Visual sensors provide exclusively uncertain and partial knowledge of a scene. In this article, we present a suitable scene knowledge representation that makes integration and fusion of new, uncertain and partial sensor measures possible. It is based on a mixture of stochastic and set membership mod ..."
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Cited by 5 (0 self)
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Visual sensors provide exclusively uncertain and partial knowledge of a scene. In this article, we present a suitable scene knowledge representation that makes integration and fusion of new, uncertain and partial sensor measures possible. It is based on a mixture of stochastic and set membership models. We consider that, for a large class of applications, an approximated representation is sufficient to build a preliminary map of the scene. Our approximation mainly results in ellipsoidal calculus by means of a normal assumption for stochastic laws and ellipsoidal over or inner bounding for uniform laws. These approximations allow us to build an efficient estimation process integrating visual data on line. Based on this estimation scheme, optimal exploratory motions of the camera can be automatically determined. Real time experimental results validating our approach are finally given.
Fault detection and isolation of LTV systems using setvalued observers
 in Proceedings of the 49th IEEE Conference on Decision and Control
, 2010
"... Abstract — This paper introduces the novel concept of using ..."
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Cited by 3 (2 self)
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Abstract — This paper introduces the novel concept of using
Computational Tools for the Verification of Hybrid Systems
"... The hybrid systems framework provides an appealing means for verifying the safety of dynamical systems. The authors address safety... ..."
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Cited by 2 (0 self)
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The hybrid systems framework provides an appealing means for verifying the safety of dynamical systems. The authors address safety...
SetMembership Filtering for DiscreteTime Systems With Nonlinear Equality Constraints
, 2009
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A SetValued Approach to FDI and FTC: Theory and Implementation Issues
"... Macau. Abstract: A complete methodology to design robust Fault Detection and Isolation (FDI) filters and Fault Tolerant Control (FTC) schemes for Linear TimeVarying (LTV) systems is proposed. The paper takes advantage of the recent advances in model invalidation using SetValued Observers (SVOs) th ..."
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Cited by 1 (1 self)
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Macau. Abstract: A complete methodology to design robust Fault Detection and Isolation (FDI) filters and Fault Tolerant Control (FTC) schemes for Linear TimeVarying (LTV) systems is proposed. The paper takes advantage of the recent advances in model invalidation using SetValued Observers (SVOs) that led to the development of FDI methods for uncertain linear timevarying systems, with promising results in terms of the time required to diagnose faults. An integration of such SVObased FDI methods with robust control synthesis is described, in order to deploy new FTC algorithms that are able to stabilize the plant under faulty environments. The FDI algorithm is assessed within a wind turbine benchmark model, using MonteCarlo simulation runs.
SetMembership Filtering with State Constraints
, 2010
"... In this paper, the problem of setmembership filtering is considered for discretetime systems with equality and inequality constraints between their state variables. We formulate the problem of setmembership filtering as finding the set of estimates that belong to an ellipsoid. A centre and a shap ..."
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In this paper, the problem of setmembership filtering is considered for discretetime systems with equality and inequality constraints between their state variables. We formulate the problem of setmembership filtering as finding the set of estimates that belong to an ellipsoid. A centre and a shape matrix of the ellipsoid are used to describe the set of estimates and the solution to the set of estimates is obtained in terms of matrix inequality. Unknown but bounded process and measurement noises are handled under the inequality constraints by using Sprocedure. We apply Finsler’s Lemma to project the set of estimates onto the constrained surface. A recursive algorithm is developed for computing the ellipsoid that guarantees to contain the true state under the state constraints, which is easily implemented by semidefinite programming via interiorpoint approach. A vehicle tracking example is provided to demonstrate the effectiveness of the proposed setmembership filtering with state equality constraints.
Nonlinear State Estimation using Imprecise Samples
"... Abstract—In state estimation theory, the general formulation is often done under assumptions of stochastic noise processes obeying well known probability distributions such as the Gaussian family. However, in many practical applications, due to the presence of high nonlinearities and unknown noise ..."
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Abstract—In state estimation theory, the general formulation is often done under assumptions of stochastic noise processes obeying well known probability distributions such as the Gaussian family. However, in many practical applications, due to the presence of high nonlinearities and unknown noise probability distributions, other methods are required. Methods such as imprecise probabilities and setmembership approaches offer robust alternative solutions to the lack of statistical information. In these frameworks, the solution to the estimation problem is no longer a posterior distribution but either a set of densities or a solution set in the state space. The main objective in this work is to take advantage of both Monte Carlo approaches and set membership methods. A novel approach to nonlinear nonGaussian state estimation problems is presented based on mixtures of imprecise samples which can be seen as unknown probability density functions with known supports. The derivation of a sequential Bayesian procedure and convergence properties of such a representation are provided. I.