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Singular H-infinity control in nonlinear systems: positive semidefinite storage functions and separation principle

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 1997年第10期7卷 881-897页

作者： Lee, TC Chen, BS Lee, TS NATL TSING HUA UNIV DEPT ELECT ENGNHSINCHU 300TAIWAN

A framework is developed for the general nonlinear H-infinity output feedback control problem, in which two major restrictions are relaxed, i.e., the non-singular penalty in H-infinity cost and the positive definite solution of Hamilton-Jacobi inequality at present state space nonlinear H-infinity control literatures. As illustrated in an example, positive semidefinite solution simplifies the structure of the H-infinity controller. Based on this framework, some sufficient conditions are derived. While specialized to linear systems, the controller reduces to the so-called central controller. (C) 1997 by John Wiley & Sons, Ltd.

关键词： H-infinity control Hamilton-Jacobi inequality positive semidefinite function

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Approximating covariance matrices estimated in multivariate models by estimated auto- and cross-covariances

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JOURNAL OF GEODESY 2010年第6期84卷 383-397页

作者： Koch, K. R. Kuhlmann, H. Schuh, W. -D. Univ Bonn Inst Geodesy & Geoinformat D-53115 Bonn Germany

Quantities like tropospheric zenith delays or station coordinates are repeatedly measured at permanent VLBI or GPS stations so that time series for the quantities at each station are obtained. The covariances of these quantities can be estimated in a multivariate linear model. The covariances are needed for computing uncertainties of results derived from these quantities. The covariance matrix for many permanent stations becomes large, the need for simplifying it may therefore arise under the condition that the uncertainties of derived results still agree. This is accomplished by assuming that the different time series of a quantity like the station height for each permanent station can be combined to obtain one time series. The covariance matrix then follows from the estimates of the auto- and cross-covariance functions of the combined time series. A further approximation is found, if compactly supported covariance functions are fitted to an estimated autocovariance function in order to obtain a covariance matrix which is representative of different kinds of measurements. The simplification of a covariance matrix estimated in a multivariate model is investigated here for the coordinates of points of a grid measured repeatedly by a laserscanner. The approximations are checked by determining the uncertainty of the sum of distances to the points of the grid. To obtain a realistic value for this uncertainty, the covariances of the measured coordinates have to be considered. Three different setups of measurements are analyzed and a covariance matrix is found which is representative for all three setups. Covariance matrices for the measurements of laserscanners can therefore be determined in advance without estimating them for each application.

关键词： Multivariate linear model positive semidefinite function Compactly supported covariance function Auto- and cross-covariance function Monte Carlo simulation Laserscanner

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SingularH∞control in nonlinear systems: positive semidefinite storage functions and separation principle

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International Journal of Robust and Nonlinear Control 1998年第10期7卷

作者： T. C. Lee B. S. Chen T. S. Lee Department of Electrical Engineering National Tsing-Hua University Hsin Chu 300 Taiwan

A framework is developed for the general nonlinear H ∞ output feedback control problem, in which two major restrictions are relaxed, i.e., the non-singular penalty in H ∞ cost and the positive definite solution of Hamilton–Jacobi inequality at present state space nonlinear H ∞ control literatures. As illustrated in an example, positive semidefinite solution simplifies the structure of the H ∞ controller. Based on this framework, some sufficient conditions are derived. While specialized to linear systems, the controller reduces to the so-called central controller. © 1997 by John Wiley & Sons, Ltd.

关键词： H∞ control Hamilton–Jacobi inequality positive semidefinite function

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