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Ural Math. J., 2015, Volume 1, Issue 1, Pages 45–54 (Mi umj4)  

This article is cited in 1 scientific paper (total in 1 paper)

Estimates of reachable sets of control systems with bilinear-quadratic nonlinearities

Tatiana F. Filippovaab, Oksana G. Matviychukab

a N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia
b Ural Federal University, Ekaterinburg, Russia

Abstract: The problem of estimating reachable sets of nonlinear impulsive control systems with quadratic nonlinearity and with uncertainty in initial states and in the matrix of system is studied. The problem is studied under uncertainty conditions with set-membership description of uncertain variables, which are taken to be unknown but bounded with given bounds. We study the case when the system nonlinearity is generated by the combination of two types of functions in related differential equations, one of which is bilinear and the other one is quadratic. The problem may be reformulated as the problem of describing the motion of set-valued states in the state space under nonlinear dynamics with state velocities having bilinear-quadratic kind. Basing on the techniques of approximation of the generalized trajectory tubes by the solutions of control systems without measure terms and using the techniques of ellipsoidal calculus we present here a state estimation algorithms for the studied nonlinear impulsive control problem bilinear-quadratic type.

Keywords: Nonlinear control systems, Impulsive control, Ellipsoidal calculus, Trajectory tubes, Estimation.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-02368
Russian Academy of Sciences - Federal Agency for Scientific Organizations
Ministry of Education and Science of the Russian Federation NS-2692.2014.1
The research was supported by the Russian Foundation for Basic Researches (RFBR) under Project 15-01-02368a, by the Project “Positional Differential Games, Hamilton-Jacobi Equations and Applications” in the framework of the Research Program “Mathematical Problems of Modern Control Theory” of the Presidium of Russian Academy of Sciences and by the Program “State Support of the Leading Scientific School” (NS-2692.2014.1).


DOI: https://doi.org/10.15826/umj.2015.1.004

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Document Type: Article
Language: English

Citation: Tatiana F. Filippova, Oksana G. Matviychuk, “Estimates of reachable sets of control systems with bilinear-quadratic nonlinearities”, Ural Math. J., 1:1 (2015), 45–54

Citation in format AMSBIB
\Bibitem{FilMat15}
\by Tatiana~F.~Filippova, Oksana~G.~Matviychuk
\paper Estimates of reachable sets of control systems with bilinear-quadratic nonlinearities
\jour Ural Math. J.
\yr 2015
\vol 1
\issue 1
\pages 45--54
\mathnet{http://mi.mathnet.ru/umj4}
\crossref{https://doi.org/10.15826/umj.2015.1.004}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. T. F. Filippova, “Vneshnie otsenki mnozhestv dostizhimosti upravlyaemoi sistemy s neopredelennostyu i kombinirovannoi nelineinostyu”, Tr. IMM UrO RAN, 23:1 (2017), 262–274  mathnet  crossref  elib
  • Ural Mathematical Journal
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