On Ellipsoidal Estimates for Reachable Sets of the Control System

  • Oxana G. MatviychukEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11548)


The problem of the ellipsoidal estimation of the reachable set of the control system under uncertainties is considered. The matrix included in the differential equations of the system dynamics is uncertain and only bounds on admissible values of this matrix coefficients are known. It is assumed that the initial states of the system are unknown but belong to a given star-shaped symmetric nondegenerate polytope. This polytope may be a non-convex set. Under such conditions, the dynamical system is a nonlinear and reachable set loses convexity property. A Minkowski function is used in the investigation to describe the trajectory tubes and their set-valued estimates. The step by step algorithm for constructing external and internal ellipsoidal estimates of reachable sets for such bilinear control systems is proposed. Numerical experiments were performed. The results of these numerical experiments are included.


Control system Ellipsoidal calculus Estimation Reachable set 


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Authors and Affiliations

  1. 1.Krasovskii Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of SciencesEkaterinburgRussia
  2. 2.Ural Federal UniversityEkaterinburgRussia

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