Differential equations of ellipsoidal state estimates in nonlinear control problems under uncertainty

Pages: 410 - 419, Issue Special, September 2011

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Tatiana Filippova - Department of Optimal Control, Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 Sofia Kovalevskaya str., Ekaterinburg 620990, Russian Federation (email)

Abstract: The properties of set-valued states of differential control systems with uncertainties in initial data are considered. It is assumed that the dynamical system has a special structure, in which the nonlinear terms in the right-hand sides of related differential equations are quadratic in state coordinates. The model of uncertainty considered here is deterministic, with setmembership description of uncertain items which are taken to be unknown but bounded with given bounds. We construct external and internal ellipsoidal estimates of reachable sets of nonlinear control system and find differential equations of proposed ellipsoidal estimates of reachable sets of nonlinear control system. Numerical simulation results are also given.

Keywords:  Differential inclusions, trajectory tubes, set-valued estimates, ellipsoidal estimation, control systems, reachable set, evolution equations
Mathematics Subject Classification:  Primary: 34A60, 49J21; Secondary: 93C41, 49K21

Received: July 2010;      Revised: February 2011;      Published: October 2011.