Abstract
A wide class of nonlinear time-invariant systems of ordinary differential equations is considered. A rather convenient algorithm for constructing a differentiable control function that performs a guaranteed transition of such systems from an initial state to a given terminal state of the state space under control constraints is proposed. A constructive criterion that guarantees the above-mentioned translation is obtained. The efficiency of this algorithm is illustrated by numerical solution of a specific practical problem.
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Kalman, R.E., Falb, P.L., and Arbib, M.A., Topics in Mathematical System Theory, Pure & Applied Mathematics Series, New York: McGraw-Hill, 1969. Translated under the title Ocherki po matematicheskoi teorii sistem, Moscow: Mir, 1971.
Walczak, S., A Note on the Controllability of Nonlinear Systems, Math. Syst. Theory, 1984, vol. 17, no. 4, pp. 351–356.
Komarov, V.A., Design of Constrained Control Signals for Nonlinear Non-autonomous Systems, Autom. Remote Control, 1984, vol. 45, no. 10, pp. 1280–1286.
Krishchenko, A.P., Controllability and Attainability Sets of Nonlinear Control Systems, Autom. Remote Control, 1984, vol. 45, no. 6, pp. 707–713.
Dirk, A., Controllability for Polynomial Systems, Lect. Notes Contr. Inf. Sci., 1984, no. 63, pp. 542–545.
Komarov, V.A., Estimates of Reachable Sets for Linear Systems, Math. USSR-Izvestiya, 1985, vol. 25, no. 1, pp. 193–206.
Balachandran, K., Global and Local Controllability of Nonlinear Systems, IEE Proc. Control Theory Appl., 1985, vol. 132, no. 1, pp. 14–17.
Benzaid, Z., Global Null Controllability of Perturbed Systems, IEE Trans. Autom. Control, 1987, no. 7, pp. 623–625.
Popova, S.N., Local Attainability for Linear Control Systems, Diff. Equat., 2003, vol. 39, no. 1, pp. 51–58.
Berdyshev, Yu.I., On the Construction of the Reachability Domain in One Nonlinear Problem, J. Comp. Syst. Sci. Int., 2006, vol. 45, no. 4, pp. 526–531.
Kvitko, A. and Yakusheva, D., On One Boundary Problem for Nonlinear Stationary Controlled System, Int. J. Control, 2019, vol. 92, no. 4, pp. 828–839. DOI: https://doi.org/10.1080/00207179.2017.1370727
Coron, J.M., Control and Nonlinearity, Providence: AMS, 2007, vol. 136.
Afanas’ev, V.N., Kolmanovskii, V.B., and Nosov, V.R., Matematicheskaya teoriya konstruirovaniya sistem upravleniya (Mathematical Theory of Control Systems Design), Moscow: Vysshaya Shkola, 1998.
Balachandran, K. and Govindaraj, V., Numerical Controllability of Fractional Dynamical Systems, Optimization, 2014, vol. 63, no. 8, pp. 1267–1279.
Krasovskii, N.N., Teoriya upravleniya dvizheniem (Theory of Motion Control), Moscow: Nauka, 1968.
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This paper was recommended for publication by M.M. Khrustalev, a member of the Editorial Board
Russian Text © The Author(s), 2020, published in Avtomatika i Telemekhanika, 2020, No. 2, pp. 48–61.
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Kvitko, A.N. A Method for Solving a Local Boundary-Value Problem for a Nonlinear Controlled System. Autom Remote Control 81, 236–246 (2020). https://doi.org/10.1134/S0005117920020046
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DOI: https://doi.org/10.1134/S0005117920020046