Topic

# Set estimation

About: Set estimation is a research topic. Over the lifetime, 306 publications have been published within this topic receiving 6392 citations.

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TL;DR: The important new feature of the proposed algorithms is their ability to ignore redundant data and the efficient data extraction property of the new algorithms is achieved with small computational effort and with improved performance when compared to the least square algorithm.

Abstract: Assuming instantaneous bounds on the noise, system parameter identification is formulated as membership set estimation problem. Sequential algorithms are constructed to estimate the membership sets of the parameters which are consistent with the measurements and the noise constraints. The important new feature of the proposed algorithms is their ability to ignore redundant data. The efficient data extraction property of the new algorithms is achieved with small computational effort and with improved performance when compared to the least square algorithm. The convergence properties and the notion of identifiability in the set theoretic context are also studied.

725 citations

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01 May 1996

TL;DR: Estimation Theory for Nonlinear Models and Set Membership Uncertainty M. Milanese, A. Vicino, and S.M. Veres, J.P. Norton.

Abstract: Overview of the Volume J. Norton. Optimal Estimation Theory for Dynamic System with Set Membership Uncertainty: An Overview M. Milanese, A. Vicino. Solving Linear Problems in the Presence of Bounded Data Perturbations B.Z. Kacewicz. A Review and a Comparison of Ellipsoidal Bounding Algorithms G. Favier, L.V.R. Arruda. On the Deadzone in System Identification K. Forsman, L. Ljung. Recursive Estimation Algorithms for Linear Models with Set Membership Error G. Belforte, T.T. Tay. Transfer Function Parameter Interval Estimation Using Recursive Least Squares in the Time and Frequency Domains P.O. Gutman. Volume-optimal Inner and Outer Ellipsoids L. Pronzato, E. Walter. Linear Interpolation and Estimation Using Interval Analysis S.M. Markov, E.D. Popova. Adaptive Approximation of Uncertainty Sets for Linear Regression Models A. Vicino, G. Zappa. Worstcase l1 Identification M. Milanese. Recursive Robust Minimax Estimation E. Walter, H. Piet-Lahanier. Robustness to Outliers of Bounded-error Estimators, Consequences on Experiment Design L. Pronzato, E. Walter. Ellipsoidal State Estimation for Uncertain Dynamical Systems T.F. Filipova, et al. Set-valued Estimation of State and Parameter Vectors within Adaptive Control-Systems V.M. Kuntsevich. Limited-complexity Polyhedric Tracking H. Piet-Lahanier, E. Walter. Parameterbounding Algorithms for Linear Errors in Variables Models S.M. Veres, J.P. Norton. Errors-invariables Models in Parameter Bounding V. Cerone. Identification of Linear Objects with Bounded Disturbances in Both Input and Output Channels Yu.A. Merkuryev. Identification of Nonlinear Statespace Models by Deterministic Search J.P. Norton, S.M. Veres. Robust Identification and Prediction for Nonlinear State-Space Models with Bounded Output Error K.J. Keesman. Estimation Theory for Nonlinear Models and Set Membership Uncertainty M. Milanese, A. Vicino. Guaranteed Nonlinear Set Estimation via Interval Analysis L. Jaulin, E. Walter. On Adaptive Control of Systems Subjected to Bounded Disturbances L.S. Zhitecki. Predictive Selftuning Control by Parameter Bounding and Worstcase Design S.M. Veres, J.P. Norton. Estimation of a Mobile Robot Localization: Geometric Approaches D. Meizel, et al. Improved Image Compression Using Bounded Error Parameter Estimation Concepts A.K. Rao. Application of OBE Algorithms to Speech Analysis, Recognition and Coding J.R. Deller Jr., et al. 2 additional articles. Index.

531 citations

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TL;DR: In this article, the output reachable estimation and safety verification problems for multilayer perceptron (MLP) neural networks are addressed, and an automated safety verification is developed based on the output reachedable set estimation result.

Abstract: In this brief, the output reachable estimation and safety verification problems for multilayer perceptron (MLP) neural networks are addressed. First, a conception called maximum sensitivity is introduced, and for a class of MLPs whose activation functions are monotonic functions, the maximum sensitivity can be computed via solving convex optimization problems. Then, using a simulation-based method, the output reachable set estimation problem for neural networks is formulated into a chain of optimization problems. Finally, an automated safety verification is developed based on the output reachable set estimation result. An application to the safety verification for a robotic arm model with two joints is presented to show the effectiveness of the proposed approaches.

273 citations

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TL;DR: In this paper, a method for parameter set estimation in which the system model is assumed to contain both parametric and nonparametric uncertainty is presented, and the parameter set estimate is guaranteed to contain the true plant.

Abstract: A method for parameter set estimation in which the system model is assumed to contain both parametric and nonparametric uncertainty is presented. In the disturbance-free case, the parameter set estimate is guaranteed to contain the parameter set of the true plant. In the presence of stochastic disturbances, the parameter set estimate obtained from finite data records is shown to have the property that it contains the true-plant parameter set with probability one as the data length tends to infinity. >

230 citations

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TL;DR: This paper presents a first study on the application of interval analysis and consistency techniques to state estimation of continuous-time systems described by nonlinear ordinary differential equations.

Abstract: This paper presents a first study on the application of interval analysis and consistency techniques to state estimation of continuous-time systems described by nonlinear ordinary differential equations. The approach is presented in a bounded-error context and the resulting methodology is illustrated by an example.

208 citations