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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2010, Volume 16, Number 1, Pages 223–232
(Mi timm539)
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This article is cited in 26 scientific papers (total in 26 papers)
Differential equations of ellipsoidal estimates for reachable sets of a nonlinear dynamical control system
T. F. Filippova Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Abstract:
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.
Received: 28.12.2009
Citation:
T. F. Filippova, “Differential equations of ellipsoidal estimates for reachable sets of a nonlinear dynamical control system”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 1, 2010, 223–232; Proc. Steklov Inst. Math. (Suppl.), 271, suppl. 1 (2010), S75–S84
Linking options:
https://www.mathnet.ru/eng/timm539 https://www.mathnet.ru/eng/timm/v16/i1/p223
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