Abstract:
In this paper we consider a reachability problem for a nonlinear affine-control system with integral constraints , which assumed to be quadratic in the control variables. Under controllability assumptions it was proved [8] that any admissible control, that steers the control system to the boundary of its reachable set, is a local solution to an optimal control problem with an integral cost functional and terminal constraints. This results in the Pontriagyn maximum principle for boundary trajectories. We propose here an numerical algorithm for computing the reachable set boundary based on the maximum principle and provide some numerical examples.
The research is supported by Russian Science Foundation, project No. 16-11-10146.
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Document Type:
Article
Language: English
Citation:
Mikhail I. Gusev, “An algorithm for computing boundary points of reachable sets of control systems under integral constraints”, Ural Math. J., 3:1 (2017), 44–51
\Bibitem{Gus17}
\by Mikhail~I.~Gusev
\paper An algorithm for computing boundary points of reachable sets of control systems under integral constraints
\jour Ural Math. J.
\yr 2017
\vol 3
\issue 1
\pages 44--51
\mathnet{http://mi.mathnet.ru/umj31}
\crossref{https://doi.org/10.15826/umj.2017.1.003}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=MR3684223}
\elib{https://elibrary.ru/item.asp?id=29728773}
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https://www.mathnet.ru/eng/umj/v3/i1/p44
This publication is cited in the following 3 articles:
Nesir Huseyin, “On the semicontinuity properties of the set of trajectories of the nonlinear control systems with integral constraints on the control functions”, International Journal of Control, 2024, 1
N. Huseyin, A. Huseyin, Kh. G. Guseinov, “On the properties of the set of trajectories of nonlinear control systems with integral constraints on the control functions”, Tr. IMM UrO RAN, 28, no. 3, 2022, 274–284
M. I. Gusev, I. V. Zykov, “On the geometry of reachable sets for control systems with isoperimetric constraints”, Proc. Steklov Inst. Math. (Suppl.), 304, suppl. 1 (2019), S76–S87
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