Geodesic
Differential equations of ellipsoidal estimates for reachable sets of a~nonlinear dynamical control system
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 1, pp. 223-232

Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of estimating trajectory tubes of a nonlinear control 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 multivalued states of dynamical systems under uncertainty.
Keywords: reachable set, trajectory tubes, set-valued estimates, differential inclusions, ellipsoidal estimation, control systems, dynamical systems. 
@article{TIMM_2010_16_1_a16,
     author = {T. F. Filippova},
     title = {Differential equations of ellipsoidal estimates for reachable sets of a~nonlinear dynamical control system},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {223--232},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2010_16_1_a16/}
}
TY  - JOUR
AU  - T. F. Filippova
TI  - Differential equations of ellipsoidal estimates for reachable sets of a~nonlinear dynamical control system
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2010
SP  - 223
EP  - 232
VL  - 16
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMM_2010_16_1_a16/
LA  - ru
ID  - TIMM_2010_16_1_a16
ER  - 
%0 Journal Article
%A T. F. Filippova
%T Differential equations of ellipsoidal estimates for reachable sets of a~nonlinear dynamical control system
%J Trudy Instituta matematiki i mehaniki
%D 2010
%P 223-232
%V 16
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMM_2010_16_1_a16/
%G ru
%F TIMM_2010_16_1_a16
T. F. Filippova. Differential equations of ellipsoidal estimates for reachable sets of a~nonlinear dynamical control system. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 1, pp. 223-232. http://geodesic.mathdoc.fr/item/TIMM_2010_16_1_a16/