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X. Rong Li - One of the best experts on this subject based on the ideXlab platform.
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Multiple-Model Estimation with Variable Structure—Part II: Model-Set Adaptation
2020Co-Authors: X. Rong LiAbstract:An important, natural, and practical approach to variable-structure multiple-Model (VSMM) estimation is the recursive adaptive Model-Set (RAMS) approach. The key to this approach is Model-Set adaptation (MSA), which is both theoret- ically and practically challenging. This paper makes theoretical contributions to MSA. Various representative problems of MSA are formulated in terms of testing hypotheses that are in general composite, -ary, multivariate, and, worst of all, not necessarily disjoint. A number of sequential solutions are presented, which are computationally highly efficient, are easy to implement, and have some desirable optimality properties. These results form a theoretical foundation for developing good, general and practical MSA algorithms. Simulation results are provided to illustrate the usefulness and effectiveness of the solutions. The theoretical results presented herein have been applied to several RAMS algorithms in the subsequent parts of this series that are generally applicable, easily implementable, and significantly superior to the best fixed-structure MM estimators available. They are also important for Model-Set comparison, choice, and design for variable-structure as well as fixed-structure MM estimation.
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CDC - Model-Set design: Uniformly distributed Models
Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, 2009Co-Authors: Yongqi Liang, X. Rong Li, Zhansheng DuanAbstract:Model-Set design is one of the most important topics of the multiple-Model approach, which is the state of the art for many estimation, control, and Modeling problems. This paper proposes a method for Model-Set design in the parameter space based on a number theoretic approach to the design of statistical experiments. Here the uncertain system is characterized by uncertain parameters that parametrize the mode space. The Model Set is designed to approximate the mode based on the discretized values of each parameter by minimizing the distribution mismatch between the Model Set and the mode in each one-dimensional projection of the mode space. Two types of uniform Model Sets are proposed, where the Models are uniformly distributed in the parameter space. Simulation examples are given to demonstrate the designs and their performance.
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General Model-Set design methods for multiple-Model approach
IEEE Transactions on Automatic Control, 2005Co-Authors: X. Rong Li, Zhanlue Zhao, Xiao-bai LiAbstract:Multiple-Model approach provides the state-of-the-art solutions to many problems involving estimation, filtering, control, and/or Modeling. One of the most important problems in the application of the multiple-Model approach is the design of the Model Set used in a multiple-Model algorithm. To our knowledge, however, it has never been addressed systematically in the literature. This paper deals with this challenging topic in a general Setting. General problems of Model-Set design are considered. A concept of a random Model is introduced. In other words, Modeling of Models used in a multiple Model (MM) algorithm as well as the true Model as random variables is proposed. Three classes of general methods for optimal design of Model Sets-by minimizing distribution mismatch, minimizing modal distance, and moment matching, respectively-are proposed. Theoretical results that address many of the associated issues are presented. Examples that demonstrate how some of these theoretical results can be used as well as their effectiveness are given. Many of the general results presented in this paper are also useful for performance evaluation of MM algorithms.
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Model-Set Design, Choice, and Comparison for Multiple-Model Approach to Hybrid Estimation
2002Co-Authors: X. Rong Li, Zhanlue Zhao, Peng Zhang, Chen HeAbstract:The most important problem in the application of the multiple-Model approach is the design of the Model Set used. This paper deals with this challenging topic in a general Setting, along with Model-Set choice and com- parison. General and representative problems of Model-Set design, choice, and comparison are considered. Modeling of Models as well as true mode as random variables is pro- posed. Several general methods for design of Model Sets are presented by minimizing distribution mismatch, minimizing modal distance, and moment matching. The concept of rel- ative efficacy of each Model in a Set and its two quantitative descriptions are introduced. Optimality criteria and perfor- mance measures for Model-Set design, choice, and compar- ison based on base-state estimation, mode estimation, mode identification, hybrid-state estimation, information metrics, and hypothesis testing are presented. Several computa- tionally efficient and easily implementable solutions of the Model-Set choice problems based on sequential hypothesis testing are presented, some of which are optimal. Examples that demonstrate how some of these theoretical results can be used as well as their effectiveness are given. Many of the general results presented in this paper are also useful for performance evaluation of MM algorithms.
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Model-Set design, choice, and comparison for multiple-Model estimation
Signal and Data Processing of Small Targets 1999, 1999Co-Authors: X. Rong Li, Chen HeAbstract:This paper deals with the design, choice, and comparison of Model Sets in the multiple-Model (MM) approach to adaptive estimation. Most representative problems of Model-Set choice and design are considered. As the basis of Model-Set choice and design, criteria for Model-Set comparison and choice based on base-state estimation, mode estimation, mode identification, hybrid-state estimation, and hypothesis testing are presented first. Several computationally efficient and easily implementable solutions of the Model- Set choice problems based on sequential hypothesis tests are presented. Some of these solutions are optimal. Their effectiveness is verified via simulation. How these criteria and result can be used for Model-Set design is demonstrated via several examples. It is also demonstrated how a probabilistic Model of possible scenarios can be constructed.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
Tong Zhou - One of the best experts on this subject based on the ideXlab platform.
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Unfalsified probability estimation for a Model Set based on frequency domain data
International Journal of Control, 2020Co-Authors: Tong ZhouAbstract:This paper deals with the problem of estimating the probability under which a Model Set is not falsified by a Set of measured plant frequency response samples. A definition of sample unfalsified probability has been proposed, and an explicit formula has been derived. Computation issues are also discussed. Moreover, an efficient algorithm has been developed for sample unfalsified probability calculation. Monte Carlo simulations show that the defined sample unfalsified probability is appropriate in the evaluation of the quality of a Model Set. Compared with the deterministic approach, simulation results suggest that the probabilistic approach is more suitable in Model Set validation.
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On the reproduction of closed-loop experimental data by an LFT perturbed Model Set
International Journal of Control, 2020Co-Authors: Tong ZhouAbstract:This paper investigates the consistency between frequency domain closed-loop experimental data and a Model Set with linear fractional unstructured uncertainties. When the number of unstable poles of the transfer function matrices (TFM) in the Model Set are identical, a necessary and sufficient condition is derived for the reproduction of experimental data. This condition is expressed as the non-positiveness of a quadratic form of the external disturbances and measurement errors, together with a linear constraint. In this derivation, it is not required that all the TFMs in the Model Set are internally stabilizable by the controller. The condition is also not necessary for the closed-loop system consisting of the nominal Model and the controller to be internally stable. It is believed that this condition is theoretically and computationally attractive in Model Set validation, no matter whether a deterministic or stochastic framework is adopted.
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Closed-loop Model Set validation under a stochastic framework
Automatica, 2002Co-Authors: Tong Zhou, Ling WangAbstract:This paper deals with probabilistic Model Set validation. It is assumed that the dynamics of a multi-input multi-output (MIMO) plant is described by a Model Set with unstructured uncertainties, and identification experiments are performed in closed loop. A necessary and sufficient condition has been derived for the consistency of the Model Set with both the stabilizing controller and closed-loop frequency domain experimental data (FDED). In this condition, only the Euclidean norm of a complex vector is involved, and this complex vector depends linearly on both the disturbances and the measurement errors. Based on this condition, an analytic formula has been derived for the sample unfalsified probability (SUP) of the Model Set. Some of the asymptotic statistical properties of the SUP have also been briefly discussed. A numerical example is included to illustrate the efficiency of the suggested method in Model Set quality evaluation.
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On the consistency between an LFT described Model Set and frequency domain data
IEEE Transactions on Automatic Control, 2001Co-Authors: Tong ZhouAbstract:The main objective of this technical note is to derive a simple necessary and sufficient condition for a linear fractional transformation (LFT) perturbed Model Set being consistent with frequency domain plant input-output data. Only discrete-time Models and unstructured Modeling errors are dealt with. Compared with the available results in which the eigenvalues of a matrix are involved, this condition is related only to the Euclidean norms of two vectors. Moreover, these vectors linearly depend on measurement errors. Some of its applications to Model Set validation have been briefly discussed. Based on this condition, an almost analytic solution has been established for Model Set validation under a deterministic framework when the measurement errors are energy bounded. Numerical simulations show that this consistency condition can lead to a significant computation cost reduction.
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Quality evaluation for a coprime factor perturbed Model Set based on frequency-domain data
IEEE Transactions on Automatic Control, 2001Co-Authors: Tong ZhouAbstract:Quality assessment is investigated under a probabilistic framework for a prescribed Model Set. The results on unfalsified probability estimation are extended from additive Modeling errors to normalized coprime factor perturbations. An analytic formula has been derived for the sample unfalsified probability. It is shown that with increasing the data length, the sample unfalsified probability converges in probability to a number which is independent of experimental data. Numerical simulations show that the proposed sample unfalsified probability is appropriate in the evaluation of the quality of a Model Set.
Rong X. Li - One of the best experts on this subject based on the ideXlab platform.
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Multiple-Model hypothesis testing using adaptive representative Model
2015 18th International Conference on Information Fusion (Fusion), 2015Co-Authors: Rong X. LiAbstract:This paper presents a multiple-Model hypothesis testing (MMHT) approach using a representative Model (RM) for detecting unknown events that may have multiple distributions. It addresses various difficulties of MMHT for composite, multivariate, nondisjoint, and mis-specified hypothesis Sets with correlated observations, and decides which region of the mode space covered by the Model Set is better. The Model-Set likelihood (MSL) based MMHT method (MMHT-MSL) is promising because of its efficiency and theoretical validity. The MSL is dominated by the likelihood of the closest-to-truth Model in the Model Set as the sample size increases. However, the multiple-Model approach usually intends to deal with all possible modes in the convex hull of the Model Set rather than only the Models in the Model Set. Consequently, when mis-specification exists, this dominating Model is not necessarily representative; that is, it is inappropriate for the Model Set rather than the region of the mode space covered by the Model Set. Our approach utilizes Model-Set adaptation (e.g., expected-mode augmentation and best Model augmentation) to improve coverage ability of the Model Set, and then searches for the Model which is closest to the truth under some criterion in the Model-Set-covered region as the RM. The RM based MMHT method (MMHT-RM) can be expected to provide a more efficient detection in the sense of minimizing the expected sample size subject to the error probability constraints. Moreover, in contrast to the MMHT-MSL, MMHT-RM is highly computationally efficient and easy to implement. Performance of MMHT-RM is evaluated for Model-Set selection problems in several scenarios. Simulation results demonstrate the effectiveness of the proposed MMHT-RM compared with MMHT-MSL.
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A General Systematic Method for Model-Set Design
IEEE Transactions on Aerospace and Electronic Systems, 2012Co-Authors: Yongqi Liang, Rong X. Li, Zhansheng DuanAbstract:Model-Set design is one of the most important topics of the multiple-Model (MM) approach, which is the state of the art for many estimation, control, and Modeling problems. The work presented here proposes a general systematic Model-Set design method in the parameter space of a system based on number theoretic (NT) methods for design of statistical experiments. The system is characterized by uncertain parameters that describe the mode space, and the Models used in the Model Set are designed to approximate the mode by minimizing distribution mismatch. Two types of F-uniform Model Sets that perform well are proposed: one by the NT methods, the other according to an F-centered discrepancy. In order to improve the performance of the F-uniform Model Sets further, two types of expected mode augmentation (EMA) are applied. Simulation examples are given and compared with results from the Monte-Carlo method to demonstrate the designs and their performance.
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Model-Set design: Uniformly distributed Models
Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, 2009Co-Authors: Yongqi Liang, Rong X. Li, Zhansheng DuanAbstract:Model-Set design is one of the most important topics of the multiple-Model approach, which is the state of the art for many estimation, control, and Modeling problems. This paper proposes a method for Model-Set design in the parameter space based on a number theoretic approach to the design of statistical experiments. Here the uncertain system is characterized by uncertain parameters that parametrize the mode space. The Model Set is designed to approximate the mode based on the discretized values of each parameter by minimizing the distribution mismatch between the Model Set and the mode in each one-dimensional projection of the mode space. Two types of uniform Model Sets are proposed, where the Models are uniformly distributed in the parameter space. Simulation examples are given to demonstrate the designs and their performance.
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Model-Set design for multiple-Model method. Part I
Proceedings of the Fifth International Conference on Information Fusion. FUSION 2002. (IEEE Cat.No.02EX5997), 2002Co-Authors: Rong X. LiAbstract:The most important problem in the application of the multiple-Model approach to estimation is the design of the Model Set. This paper deals with this challenging topic in a general Setting. Modeling of Models as well as true mode as random variables is proposed. Several general methods for design of Model Sets, along with the initial Model probabilities, are presented. They include distribution approximation, minimizing mismatch between mode and Models, and moment matching. Examples that demonstrate how the general results presented here can be applied are presented in Part II.
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Multiple-Model estimation with variable structure. II. Model-Set adaptation
IEEE Transactions on Automatic Control, 2000Co-Authors: Rong X. LiAbstract:For pt.I see ibid., vol.41, p.487-93 (1996). An important, natural, and practical approach to variable-structure multiple-Model (VSMM) estimation is the recursive adaptive Model-Set (RAMS) approach. The key to this approach is Model-Set adaptation (MSA), which is both theoretically and practically challenging. This paper makes theoretical contributions to MSA. Various representative problems of MSA are formulated in terms of testing hypotheses that are in general composite, N-ary, multivariate, and, worst of all, not necessarily disjoint. A number of sequential solutions are presented, which are computationally highly efficient, are easy to implement, and have some desirable optimality properties. These results form a theoretical foundation for developing good, general and practical MSA algorithms. Simulation results are provided to illustrate the usefulness and effectiveness of the solutions. The theoretical results presented herein have been applied to several RAMS algorithms in the subsequent parts of this series that are generally applicable, easily implementable, and significantly superior to the best fixed-structure MM estimators available. They are also important for Model-Set comparison, choice, and design for variable-structure as well as fixed-structure MM estimation.
Brian Scassellati - One of the best experts on this subject based on the ideXlab platform.
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IROS - The HRC Model Set for Human-Robot Collaboration Research
2018 IEEE RSJ International Conference on Intelligent Robots and Systems (IROS), 2018Co-Authors: Sofya Zeylikman, Sarah Widder, Alessandro Roncone, Olivier Mangin, Brian ScassellatiAbstract:In this paper, we present a Model Set for designing human-robot collaboration (HRC) experiments. It targets a common scenario in HRC, which is the collaborative assembly of furniture, and it consists of a combination of standard components and custom designs. With this work, we aim at reducing the amount of work required to Set up and reproduce HRC experiments, and we provide a unified framework to facilitate the comparison and integration of contributions to the field. The Model Set is designed to be modular, extendable, and easy to distribute. Importantly, it covers the majority of relevant research in HRC, and it allows tuning of a number of experimental variables that are particularly valuable to the field. Additionally, we provide a Set of software libraries for perception, control and interaction, with the goal of encouraging other researchers to proactively contribute to our work.
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The HRC Model Set for Human-Robot Collaboration Research
2018 IEEE RSJ International Conference on Intelligent Robots and Systems (IROS), 2018Co-Authors: Sofya Zeylikman, Sarah Widder, Alessandro Roncone, Olivier Mangin, Brian ScassellatiAbstract:In this paper, we present a Model Set for designing human-robot collaboration (HRC) experiments. It targets a common scenario in HRC, which is the collaborative assembly of furniture, and it consists of a combination of standard components and custom designs. With this work, we aim at reducing the amount of work required to Set up and reproduce HRC experiments, and we provide a unified framework to facilitate the comparison and integration of contributions to the field. The Model Set is designed to be modular, extendable, and easy to distribute. Importantly, it covers the majority of relevant research in HRC, and it allows tuning of a number of experimental variables that are particularly valuable to the field. Additionally, we provide a Set of software libraries for perception, control and interaction, with the goal of encouraging other researchers to proactively contribute to our work.
X.r. Li - One of the best experts on this subject based on the ideXlab platform.
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Probabilistic Model distortion measure and its application to Model-Set design of multiple Model approach
Conference Record of the Thirty-Eighth Asilomar Conference on Signals Systems and Computers 2004., 2004Co-Authors: Zhanlue Zhao, X.r. LiAbstract:In parameter estimation and filtering, Model approximation is quite common in engineering research and development. These approximations distort the original relation between the parameter of interest and the observation and cause the performance deterioration. It is crucial to have a measure to appraise these approximations. In this paper, we analyze the structure of the parameter inference and clarify its ingrained vagueness. Accordingly, we apprehend the commensuration between the Model distortion and the difference between two probability density functions. We work out a distortion measure, and it turns out that the Kullback-Leibler (K-L) divergence can serve this purpose. We apply the K-L divergence as a distortion measure to Model Set design for multiple Model estimation. We demonstrate that the K-L divergence is a measure of significance for estimation performance deterioration, and has high potential for the development of highly adaptive algorithms.
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Model-Set design for multiple-Model method. II. Examples
Proceedings of the Fifth International Conference on Information Fusion. FUSION 2002. (IEEE Cat.No.02EX5997), 2002Co-Authors: X.r. Li, Zhanlue Zhao, Peng Zhang, Chen HeAbstract:This paper presents several examples that illustrate how the theoretical results presented in part I and other work can be applied, along with a demonstration of their effectiveness, in the context of MM estimation for air traffic control surveillance. Model-Set design and choice examples are presented. The importance and usefulness of Modeling true mode and Models as random variables are demonstrated. The construction of such a probabilistic Model is also demonstrated.
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Model-Set adaptation in variable-structure MM estimation by hypothesis testing
Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207), 1998Co-Authors: X.r. LiAbstract:The key component in variable-structure multiple-Model (MM) estimation is Model-Set adaptation (MSA). This paper formulates MSA as hypothesis testing problems and provides effective solutions, which have some desirable optimality properties. The hypotheses tested are in general composite, N-ary, multivariate, and worst of all, not necessarily disjoint. The results form a theoretical foundation and guideline for developing good and practical MSA algorithms.
