Geodesic
Construction of the reachable set for a two-dimensional bilinear impulsive control system
The Bulletin of Irkutsk State University. Series Mathematics, Tome 15 (2016), pp. 3-16 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper deals with a problem of construction of the reachable set for an impulsive control system with trajectories of bounded variation and impulsive controls (regular vector measures). The considered control system has a bilinear structure relative to the control variable. A method for constructing of the boundary of the reachable set is proposed. This method is based on using of special impulsive optimal control problems and Lyapunov type functions. These functions are strongly monotone relative to the impulsive control system. Presented results are illustrated by a numerical example. An algorithm of numerical approximation of reachable sets for nonlinear impulsive control systems is discussed. This algorithm is realized in the Scientific Python environment.
Keywords: measure-driven impulsive control system, trajectories of bounded variation, reachable set, monotone of Lyapunov type functions, numerical methods. 
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D. V. Apanovich; V. A. Voronov; O. N. Samsonyuk. Construction of the reachable set for a two-dimensional bilinear impulsive control system. The Bulletin of Irkutsk State University. Series Mathematics, Tome 15 (2016), pp. 3-16. http://geodesic.mathdoc.fr/item/IIGUM_2016_15_a0/

[1] Apanovich D. V., Voronov V. A., “Numerical approximation of reachable sets for nonlinear impulsive control systems”, Abstracts of Russian Conference with International Participation dedicated to the memory of prof. N. V. Azbelev and prof. E. L. Tonkov (Izhevsk, Russia, June 9–11, 2015), 24–25

[2] Apanovich D. V., Voronov V. A., “Numerical approximation of the non-simply connected reachable set for a nonlinear impulsive control system”, Abstract of 3rd Russian–Mongolian Conference of Young Scientist on Math Modelling and Information Technology (Irkutsk, Russia–Hanh, Mongolia, June 23–30, 2015), 17

[3] Dykhta V. A., Samsonyuk O. N., Optimal Impulsive Control with Applications, Fizmatlit, M., 2000

[4] Zavalishchin S. T., Sesekin A. N., Impulse Processes: Models and Applications, Nauka, M., 1991 | MR

[5] Miller B. M., Rubinovich E. Ya., Optimization of Dynamic Systems with Impulsive Controls, Nauka, M., 2005

[6] Samsonyuk O. N., “Monotonicity of Lyapunov Type Functions for Impulsive Control Systems”, The bulletin of Irkutsk state university. Mathematics, 7 (2014), 104–123 | Zbl

[7] Samsonyuk O. N., “Invariant Sets for the Nonlinear Impulsive Control Systems”, Autom. Remote Control, 76:3 (2015), 405–418 | DOI | MR | Zbl

[8] F. H. Clarke, Yu. S. Ledyaev, R. J. Stern, P. R. Wolenski, Nonsmooth Analysis and Control Theory, Springer-Verlag, N.Y., 1998 | MR | Zbl

[9] V. Dykhta, O. Samsonyuk, “Some applications of Hamilton–Jacobi inequalities for classical and impulsive optimal control problems”, European Journal of Control, 17 (2011), 55–69 | DOI | MR | Zbl

[10] R. B. Vinter, Optimal Control, Birkhauser, Boston, 2000 | MR | Zbl