Results 1  10
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27
Robust Solutions To LeastSquares Problems With Uncertain Data
, 1997
"... . We consider leastsquares problems where the coefficient matrices A; b are unknownbutbounded. We minimize the worstcase residual error using (convex) secondorder cone programming, yielding an algorithm with complexity similar to one singular value decomposition of A. The method can be interpret ..."
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Cited by 146 (12 self)
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. We consider leastsquares problems where the coefficient matrices A; b are unknownbutbounded. We minimize the worstcase residual error using (convex) secondorder cone programming, yielding an algorithm with complexity similar to one singular value decomposition of A. The method can be interpreted as a Tikhonov regularization procedure, with the advantage that it provides an exact bound on the robustness of solution, and a rigorous way to compute the regularization parameter. When the perturbation has a known (e.g., Toeplitz) structure, the same problem can be solved in polynomialtime using semidefinite programming (SDP). We also consider the case when A; b are rational functions of an unknownbutbounded perturbation vector. We show how to minimize (via SDP) upper bounds on the optimal worstcase residual. We provide numerical examples, including one from robust identification and one from robust interpolation. Key Words. Leastsquares, uncertainty, robustness, secondorder cone...
On validation and invalidation of biological models
, 2009
"... which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Background: Very frequently the same biological system is described by several, sometimes competing mathematical models. This usually creates confusion around their validity, i ..."
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Cited by 6 (0 self)
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which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Background: Very frequently the same biological system is described by several, sometimes competing mathematical models. This usually creates confusion around their validity, ie, which one is correct. However, this is unnecessary since validity of a model cannot be established; model validation is actually a misnomer. In principle the only statement that one can make about a system model is that it is incorrect, ie, invalid, a fact which can be established given appropriate experimental data. Nonlinear models of high dimension and with many parameters are impossible to invalidate through simulation and as such the invalidation process is often overlooked or ignored. Results: We develop different approaches for showing how competing ordinary differential equation (ODE) based models of the same biological phenomenon containing nonlinearities and parametric uncertainty can be invalidated using experimental data. We first emphasize the strong interplay between system identification and model invalidation and we describe a method for obtaining a lower bound on the error between candidate model predictions and data. We then turn
Robust Flutter Margin Analysis That Incorporates Flight Data
, 1998
"... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 CHAPTER 1 INT ..."
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Cited by 6 (2 self)
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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 CHAPTER 1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 CHAPTER 2 ROBUST STABILITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1 Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3 Small Gain Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
Statistical Plant Set Estimation Using SchroederPhased Multisinusoidal Input Design
 J. APPLIED MATHEMATICS AND COMPUTATION
, 1992
"... In this paper, a frequency domain method is developed for plant set estimation. The estimation of a plant rather than a point estimate is required to support many methods of modern robust control design. The approach here is based on using a phased input design which has the special property of pl ..."
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Cited by 6 (2 self)
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In this paper, a frequency domain method is developed for plant set estimation. The estimation of a plant rather than a point estimate is required to support many methods of modern robust control design. The approach here is based on using a phased input design which has the special property of placing input energy only at the discrete frequency points used in the computation. A detailed of statistical properties of the frequency domain estimator is given leading to exact expressions for the probability distribution of the estimation error, and many important properties. It is shown that for any nominal parametric plant estimate, one can use these results to construct an overbound on the additive uncertainty to any prescribed statistical confidence. The "soft" bound thus obtained can be used to replace "hard" bounds presently used in many robust control analysis and synthesis methods.
Suboptimal Feedback Control by a Scheme of Iterative Identification and Control Design
, 1997
"... In this paper a framework for an iterative procedure of identification and robust control design is introduced wherein the robust performance is monitored during the subsequent steps of the iterative scheme. By monitoring the performance via a modelbased approach, the possibility to guarantee pe ..."
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Cited by 5 (0 self)
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In this paper a framework for an iterative procedure of identification and robust control design is introduced wherein the robust performance is monitored during the subsequent steps of the iterative scheme. By monitoring the performance via a modelbased approach, the possibility to guarantee performance improvement in the iterative scheme is being employed. In order to monitor achieved performance (for a present controller) and to guarantee robust performance (for a future controller), an uncertainty set is used where the uncertainty structure is chosen in terms of model perturbations in the dual Youla parametrization. This uncertainty structure is shown to be particularly suitable for the control performance measure that is considered. The model uncertainty set can be identified by an uncertainty estimation procedure on the basis of closedloop experimental data. To obtain performance robustness, robust control design tools are used to synthesise controllers on the basis of ...
SemiBlind Model (In)Validation with Applications to Texture Classification
, 2005
"... This paper addresses the problem of model (in)validation of linear discrete–time (LTI) models subject to unstructured LTI uncertainty, using frequency–domain data corrupted by additive noise. Contrary to the case usually considered in the (deterministic) invalidation literature, here the input to th ..."
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Cited by 4 (3 self)
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This paper addresses the problem of model (in)validation of linear discrete–time (LTI) models subject to unstructured LTI uncertainty, using frequency–domain data corrupted by additive noise. Contrary to the case usually considered in the (deterministic) invalidation literature, here the input to the system has an unknown phase. This problem arises naturally for instance in the context of validating systems subject to unknown time–delays, or in cases where only the spectral power density of the (in this case stochastic) input is known. It can be shown that this leads to a generically NP hard minimization problem. The main result of this paper is an efficient, LMI based convex relaxation of the problem. These results are illustrated with a non–trivial problem: classification of textured images.
Parameterization Of Model Validating Sets For Uncertainty Bound Optimizations
, 1998
"... Given measurement data, a nominal model and a linear fractional transformation uncertainty structure with an allowance on unknown but bounded exogenous disturbances, easily computable tests for the existence of a model validating uncertainty set are given. Under mild conditions, these tests are nece ..."
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Cited by 2 (1 self)
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Given measurement data, a nominal model and a linear fractional transformation uncertainty structure with an allowance on unknown but bounded exogenous disturbances, easily computable tests for the existence of a model validating uncertainty set are given. Under mild conditions, these tests are necessary and su#cient for the case of complex, nonrepeated, blockdiagonal structure. For the more general case which includes repeated and#or real scalar uncertainties, the tests are only necessary but become su#cient if a collinearity condition is also satis#ed. With the satisfaction of these tests, it is shown that a parameterization of all model validating sets of plant models is possible. The new parameterization is used as a basis for a systematic way to construct or perform uncertainty tradeo# with model validating uncertainty sets whichhave speci#c linear fractional transformation structure for use in robust control design and analysis. An illustrative example which includes a compariso...
Analysis of a Scheme for Iterated Identification and Control
, 1994
"... . This paper presents analysis of a scheme for iterated identification and control design. The approach is based on least squares identification in closed loop and pole placement design. It has previously been shown that the criteria for control and identification are the same provided that the data ..."
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. This paper presents analysis of a scheme for iterated identification and control design. The approach is based on least squares identification in closed loop and pole placement design. It has previously been shown that the criteria for control and identification are the same provided that the data filters are chosen properly. The iterated scheme may be viewed as a recursion in model parameters. Each step consists of system identification and control design. Interesting questions are then: What are the fix points? Are the fix points stable? These questions are investigated for some simple examples. Relations to other problems like model reduction and adaptive control are also discussed. Keywords. Adaptive Control, Control Design, Identification, Least Squares Estimation, Model reduction, Pole Placement Control, Prediction Error Methods. 1. INTRODUCTION A sensible formulation of an identification problem should consider the ultimate use of the model. In control system design we are in...
An LPV Approach to Synthesizing Robust Active Vision Systems
 In IEEE Conference on Decision and Control
, 2000
"... Recent hardware developments have rendered controlled active vision a viable option for a broad range of practical problems. However, realizing this potential requires having a framework for synthesizing robust active vision systems, capable of moving beyond carefully controlled environments. Recent ..."
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Cited by 2 (1 self)
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Recent hardware developments have rendered controlled active vision a viable option for a broad range of practical problems. However, realizing this potential requires having a framework for synthesizing robust active vision systems, capable of moving beyond carefully controlled environments. Recent work has shown that this can be achieved by combining robust computer vision and control techniques. However, in some cases robustness is achieved at the expense of performance. In this paper we show that this performance loss can be avoided by recasting the problem into a Linear Parameter Varying (LPV) form and using recently developed robust identification and control tools for this class of problems. These results are experimentally validated using a Bisight robotic head. 1 Introduction and Motivation Recent hardware advances have rendered visual feedback a viable option for a very diverse spectrum of applications ranging from MEMS manufacture[7] to assisting individuals with disabilit...
Mixed Time/FrequencyDomain Based Robust
"... A new robust identification framework that incorporates both time and frequency domain data is proposed. his framework avoids situations where a good data fit in one domain leads to poor fitting in the other. Key Words—Robust identification; control oriented identification; interpolation; convex opt ..."
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Cited by 2 (2 self)
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A new robust identification framework that incorporates both time and frequency domain data is proposed. his framework avoids situations where a good data fit in one domain leads to poor fitting in the other. Key Words—Robust identification; control oriented identification; interpolation; convex optimization; Linear Matrix Inequalities. Abstract—In this paper we propose a new robust identification framework that combines both frequency and timedomain experimental data. The main result of the paper shows that the problem of obtaining a nominal model consistent with the experimental data and bounds on the identification error can be recast as a constrained finitedimensional convex optimization problem that can be efficiently solved using Linear Matrix Inequalities techniques. This approach, based upon a generalized interpolation theory, contains as special cases the Carathéodory—Fejér (purely timedomain) and Nevanlinna— Pick (purely frequencydomain) problems. The proposed procedure interpolates the frequency and time domain experimental data while restricting the identified system to be in an a priori given class of models, resulting in a nominal model consistent with both sources of data. Thus, it is convergent and optimal up to a factor of two (with respect to central algorithms). � 1998