Differential equations for ellipsoidal estimates for reachable sets of a nonlinear dynamical control system

The problem of estimating trajectory tubes of a nonlinear control dynamical system with uncertainty in initial data is considered. It is assumed that the dynamical system has a special structure, in which nonlinear terms are quadratic in phase coordinates and the values of the uncertain initial stat...

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Bibliographic Details
Published inProceedings of the Steklov Institute of Mathematics Vol. 271; no. Suppl 1; pp. 75 - 84
Main Author Filippova, T. F.
Format Journal Article
LanguageEnglish
Published Dordrecht SP MAIK Nauka/Interperiodica 01.10.2010
Subjects
Mathematics
Mathematics and Statistics
dynamical systems
ellipsoidal estimation
reachable set
control systems
trajectory tubes
set-valued estimates
differential inclusions
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ISSN0081-5438
1531-8605
DOI10.1134/S0081543810070072

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Summary:The problem of estimating trajectory tubes of a nonlinear control dynamical system with uncertainty in initial data is considered. It is assumed that the dynamical system has a special structure, in which nonlinear terms are quadratic in phase coordinates and the values of the uncertain initial states and admissible controls are subject to ellipsoidal constraints. Differential equations are found that describe the dynamics of the ellipsoidal estimates of reachable sets of the nonlinear dynamical system under consideration. To estimate reachable sets of the nonlinear differential inclusion corresponding to the control system, we use results from the theory of ellipsoidal estimation and the theory of evolution equations for set-valued states of dynamical systems under uncertainty.
ISSN:0081-5438
1531-8605
DOI:10.1134/S0081543810070072