Abstract:
We investigate the convexity of the reachable sets for some of the coordinates of nonlinear systems with integral constraints on the control at small time intervals. We have proved sufficient convexity conditions in the form of constraints on the asymptotics of the eigenvalues of the Gramian of the controllability of a linearized system for some of the coordinates. There are two nonlinear third-order systems under study as examples. The system linearized along a trajectory generated by zero control is uncontrollable, and the system in the other example is completely controllable. We investigate the sufficient conditions for convexity of projection of reachable sets. Numerical modeling has been carried out, demonstrating the non-convexity of some projections even for small time intervals.
Keywords:
nonlinear control systems, reachable sets, integral constraints, convexity, linearization, small time interval, asympotics.
Citation:
I. O. Osipov, “On the convexity of the reachable set with respect to a part of coordinates at small time intervals”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 31:2 (2021), 210–225
\Bibitem{Osi21}
\by I.~O.~Osipov
\paper On the convexity of the reachable set with respect to a part of coordinates at small time intervals
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2021
\vol 31
\issue 2
\pages 210--225
\mathnet{http://mi.mathnet.ru/vuu765}
\crossref{https://doi.org/10.35634/vm210204}
Linking options:
https://www.mathnet.ru/eng/vuu765
https://www.mathnet.ru/eng/vuu/v31/i2/p210
This publication is cited in the following 4 articles:
Ivan O. Osipov, “Convexity of reachable sets of quasilinear systems”, Ural Math. J., 9:2 (2023), 141–156
Mikhail Gusev, Ivan Osipov, Lecture Notes in Computer Science, 13930, Mathematical Optimization Theory and Operations Research, 2023, 362
M. I. Gusev, I. O. Osipov, “O zadache lokalnogo sinteza dlya nelineinykh sistem s integralnymi ogranicheniyami”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 32:2 (2022), 171–186
Mikhail Gusev, Ivan Osipov, 2022 16th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference), 2022, 1
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