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47
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.
Robust Filtering for DiscreteTime Systems with Bounded Noise and Parametric Uncertainty
 IEEE Trans. Aut. Control
, 2001
"... This paper presents a new approach to finitehorizon guaranteed state prediction for discretetime systems affected by bounded noise and unknownbutbounded parameter uncertainty. Our framework handles possibly nonlinear dependence of the statespace matrices on the uncertain parameters. The main re ..."
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Cited by 25 (4 self)
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This paper presents a new approach to finitehorizon guaranteed state prediction for discretetime systems affected by bounded noise and unknownbutbounded parameter uncertainty. Our framework handles possibly nonlinear dependence of the statespace matrices on the uncertain parameters. The main result is that a minimal confidence ellipsoid for the state, consistent with the measured output and the uncertainty description, may be recursively computed in polynomial time, using interiorpoint methods for convex optimization. With n states, l uncertain parameters appearing linearly in the statespace matrices, with rankone matrix coefficients, the worstcase complexity grows as O(l(n + l) 3:5 ). With unstructured uncertainty in all system matrices, the worstcase complexity reduces to O(n 3:5 ).
Simultaneous Localisation and Map Building
, 1997
"... This thesis examines the problem of localising an Autonomous Guided Vehicle (AGV) travelling in an unknown environment. In this problem, the AGV faces the dual task of modeling the environment and simultaneously localising its position within it. The Simultaneous Localisation and Map Building (SLAM) ..."
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Cited by 22 (0 self)
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This thesis examines the problem of localising an Autonomous Guided Vehicle (AGV) travelling in an unknown environment. In this problem, the AGV faces the dual task of modeling the environment and simultaneously localising its position within it. The Simultaneous Localisation and Map Building (SLAM) problem is currently one of the most important goals of AGV research. Solving this problem would allow anAGV to be deployed easily, with very little initial preparation. The AGV would also be exible and able to cope with modi cations in the environment. A solution to the SLAM problem would enable an AGV to would be truly \autonomous." The thesis examines the SLAM problem from an estimation theoretic point ofview. The estimation approach provides a rigorous framework for the analysis and has also proven to be successful in actual applications. The most signi cant contribution of this thesis is to provide, for the rst time, a detailed development of the theory of the SLAM problem. It is shown that correlations arise between errors in the vehicle and the map estimates, and these correlations are identi ed as fundamentally important to the solution of the SLAM problem. It is demonstrated that ignoring these correlations results in the loss of the fundamental structure of the SLAM problem and leads to inconsistency in map
A Framework for StateSpace Estimation with Uncertain Models
 IEEE Trans. Auto. Contr
, 2001
"... This paper develops a framework for statespace estimation when the parameters of the underlying linear model are subject to uncertainties. Compared with existing robust filters, the proposed filters perform regularization rather than deregularization. It is shown that, under certain stabilizabilit ..."
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Cited by 19 (1 self)
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This paper develops a framework for statespace estimation when the parameters of the underlying linear model are subject to uncertainties. Compared with existing robust filters, the proposed filters perform regularization rather than deregularization. It is shown that, under certain stabilizability and detectability conditions, the steadystate filters are stable and that, for quadraticallystable models, the filters guarantee a bounded error variance. Moreover, the resulting filter structures are similar to various (time and measurementupdate, prediction, and information) forms of the Kalman filter, albeit ones that operate on corrected parameters rather than on the given nominal parameters. Simulation results and comparisons with H1 , guaranteedcost, and setvalued state estimation filters are provided.
Parallelotopic and Practical Observers for Nonlinear Uncertain Systems
 Int. Journal. Control
, 2002
"... For a class of dynamical systems, with uncertain nonlinear terms considered as "unknown inputs", we give sufficient conditions for observability. We show also that there does not exist any exact observer independent of the unknown inputs. Under the additional assumption that the uncertaint ..."
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Cited by 13 (0 self)
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For a class of dynamical systems, with uncertain nonlinear terms considered as "unknown inputs", we give sufficient conditions for observability. We show also that there does not exist any exact observer independent of the unknown inputs. Under the additional assumption that the uncertainty is bounded, we build practical observers whose error converges exponentially towards an arbitrarily small neighborhood of the origin. Under the hypothesis that bounds are available for the uncertain terms, we build parallelotopic observers providing timevarying bounds for the state variables, even when the system is not observable for unknown inputs These results are illustrated on a biological model of a structured population.
... 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...
WorstCase Simulation of Uncertain Systems
, 1999
"... In this paper we consider the problem of worstcase simulation for a discretetime system with structured uncertainty. The approach is based on the recursive computation of ellipsoids of condence for the system state, based on semidefinite programming. ..."
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Cited by 8 (3 self)
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In this paper we consider the problem of worstcase simulation for a discretetime system with structured uncertainty. The approach is based on the recursive computation of ellipsoids of condence for the system state, based on semidefinite programming.
Tracking of TimeVarying Parameters using Optimal Bounding Ellipsoid Algorithms
 Proc., 34th Annual Allerton Conf. Communication, Control and Computing, University of Illinois, UrbanaChampaign, Oct 24
, 1996
"... This paper analyzes the performance of an optimal bounding ellipsoid (OBE) algorithm for tracking timevarying parameters with incrementally bounded time variations. A linear statespace model is used, with the timevarying parameters represented by the state vector. The OBE algorithm exhibits a sel ..."
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Cited by 6 (5 self)
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This paper analyzes the performance of an optimal bounding ellipsoid (OBE) algorithm for tracking timevarying parameters with incrementally bounded time variations. A linear statespace model is used, with the timevarying parameters represented by the state vector. The OBE algorithm exhibits a selective update property for the time and observationupdate equations, and necessary and sufficient conditions for state tracking are derived. The interpretability of the optimization criterion is also investigated along with simulation results. 1 Introduction Tracking of time varying parameters is an important problem, both from theoretical as well as practical viewpoints, in adaptive signal processing, communication and control systems. An elegant, convenient and general framework for formulating the problem is provided by linear statespace equations. In this paper, we use the discretetime state equation framework and present an optimal bounding ellipsoid (OBE) algorithm for tracking tim...
On comparing statistical and setbased methods in sensor data fusion
 In Proc. IEEE Int. Conf. Robotics and Automation
, 1993
"... ..."
Guaranteed Mobile Robot Tracking Using Interval Analysis
"... : The problem considered here is state estimation in the presence of bounded process and measurement noise. A new nonlinear state estimator, based on interval analysis and the notion of set inversion, is applied to robot localization and tracking. This estimator evaluates a set guaranteed to contain ..."
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Cited by 4 (4 self)
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: The problem considered here is state estimation in the presence of bounded process and measurement noise. A new nonlinear state estimator, based on interval analysis and the notion of set inversion, is applied to robot localization and tracking. This estimator evaluates a set guaranteed to contain all values of the state that are consistent with the available observations, given the noise bounds and some possibly very large set containing the initial value of the state. Three situations are considered to illustrate the properties of the estimator. Keywords: Boundederror estimation, Interval analysis, Robot localization, Robot tracking, State estimation. 1 Introduction Much of recent research in robotics has been devoted to increasing autonomy, e.g., by adding sensors, mobility and decision capability. To be autonomous, robots must be able to estimate their present state from available prior information and measurements. The problem to be considered here is the autonomous localizati...