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Type Functional (type + functional)

Distribution by Scientific Domains
Mathematics and Statistics60%

Selected Abstracts

State-feedback adaptive tracking of linear systems with input and state delays

INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 6 2009
Boris Mirkin
Abstract A state-feedback Lyapunov-based design of direct model reference adaptive control is developed for a class of linear systems with input and state delays based only on lumped delays without so-called distributed-delay blocks. The design procedure is based on the concept of reference trajectory prediction, and on the formulation of an augmented error. We propose a controller parametrization that attempts to anticipate the future states. An appropriate Lyapunov,Krasovskii type functional is found for the design and the stability analysis. A simulation example illustrates the new controller. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Output-feedback co-ordinated decentralized adaptive tracking: The case of MIMO subsystems with delayed interconnections

INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 8 2005
Boris M. Mirkin
Abstract Exact decentralized output-feedback Lyapunov-based designs of direct model reference adaptive control (MRAC) for linear interconnected delay systems with MIMO subsystems are introduced. The design process uses a co-ordinated decentralized structure of adaptive control with reference model co-ordination which requires an exchange of signals between the different reference models. It is shown that in the framework of the reference model co-ordination zero residual tracking error is possible, exactly as in the case with SISO subsystems. We develop decentralized MRAC on the base of a priori information about only the local subsystems gain frequency matrices without additional a priori knowledge about the full system gain frequency matrix. To achieve a better adaptation performance we propose proportional, integral time-delayed adaptation laws. The appropriate Lyapunov,Krasovskii type functional is suggested to design the update mechanism for the controller parameters, and in order to prove stability. Two different adaptive DMRAC schemes are proposed, being the first asymptotic exact zero tracking results for linear interconnected delay systems with MIMO subsystems. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Theory & Methods: Data Sharpening for Hazard Rate Estimation

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 3 2002
Gerda Claeskens
Data sharpening is a general tool for enhancing the performance of statistical estimators, by altering the data before substituting them into conventional methods. In one of the simplest forms of data sharpening, available for curve estimation, an explicit empirical transformation is used to alter the data. The attraction of this approach is diminished, however, if the formula has to be altered for each different application. For example, one could expect the formula for use in hazard rate estimation to differ from that for straight density estimation, since a hazard rate is a ratio,type functional of a density. This paper shows that, in fact, identical data transformations can be used in each case, regardless of whether the data involve censoring. This dramatically simplifies the application of data sharpening to problems involving hazard rate estimation, and makes data sharpening attractive. [source]

Existence and convergence for quasi-static evolution in brittle fracture

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 10 2003
Gilles A. Francfort
This paper investigates the mathematical well-posedness of the variational model of quasi-static growth for a brittle crack proposed by Francfort and Marigo in [15]. The starting point is a time discretized version of that evolution which results in a sequence of minimization problems of Mumford and Shah type functionals. The natural weak setting is that of special functions of bounded variation, and the main difficulty in showing existence of the time-continuous quasi-static growth is to pass to the limit as the time-discretization step tends to 0. This is performed with the help of a jump transfer theorem which permits, under weak convergence assumptions for a sequence {un} of SBV-functions to its BV-limit u, to transfer the part of the jump set of any test field that lies in the jump set of u onto that of the converging sequence {un}. In particular, it is shown that the notion of minimizer of a Mumford and Shah type functional for its own jump set is stable under weak convergence assumptions. Furthermore, our analysis justifies numerical methods used for computing the time-continuous quasi-static evolution. © 2003 Wiley Periodicals, Inc. [source]