Estimation of Star-Shaped Reachable Sets of Nonlinear Control Systems

  • Tatiana F. Filippova
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10665)


The problem of estimating reachable sets of nonlinear dynamical control systems with uncertainty in initial states is studied when it is assumed that only the bounding set for initial system positions is known and any additional statistical information is not available. We study the case when the system nonlinearity is generated from one side by bilinear terms in the matrix elements included in the state velocities and from the other side by quadratic functions in the right-hand part of system differential equations. Using results of the theory of trajectory tubes of control systems and techniques of differential inclusions theory and also results of ellipsoidal calculus we find set-valued estimates of reachable sets of such nonlinear uncertain control system.


Control systems Nonlinearity Uncertainty Ellipsoidal estimates 



The research was supported by Russian Science Foundation (RSF Project No.16-11-10146).


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© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Krasovskii Institute of Mathematics and Mechanics of RASEkaterinburgRussian Federation

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