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Convexity of Reachable Sets of a Smooth Linear Control System in Phase Variables

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Abstract

A smooth control system that is linear in phase variables is studied. Sufficient conditions for the convexity of its reachable set are derived so that the Pontryagin maximum principle can be effectively applied to study the control system.

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REFERENCES

  1. Lee, E.B. and Markus, L., Foundations of Optimal Control Theory, New York: Wiley, 1967. Translated under the title Osnovy teorii optimal'nogo upravleniya, Moscow: Mir, dy1973.

    Google Scholar 

  2. Brockett, R.W., On the Reachable Set for Bilinear Systems, Lect. Notes Econ. Math. Syst., 1975, vol. 111, pp. 54–63.

    Google Scholar 

  3. Andreev, Yu.N., Differential Geometric Methods in Control Theory, Avtom. Telemekh., 1982, no.10, pp. 5–46.

    Google Scholar 

  4. Bressan, A., Directional Convexity and Finite Optimality Conditions, J. Math. Anal. Appl., 1987, vol. 125, no. 1, pp. 234–246.

    Google Scholar 

  5. Krener, A.J. and Schättler, H., The Structure of Small-Time Reachable Sets in Low Dimensions, SIAM J. Contr. Optimiz., 1989, vol. 27, no. 1, pp. 120–147.

    Google Scholar 

  6. Topunov, M.V., Convexity of the Reachable Set of a Quasi-Commutative Bilinear System, Avtom. Telemekh., 2003, no. 8, pp. 44–53.

  7. Aubin, J.P. and Ekeland, I., Applied Nonlinear Analysis, New York: Wiley, 1984. Translated under the title Prikladnoi nelineinyi analiz, Moscow: Mir, 1988.

    Google Scholar 

  8. Topunov, M.V., Convexity of the Reachable Set of a Bilinear Control System, Prikl. Mat. Mekh., 2003, vol. 63, no. 5, pp. 752–758.

    Google Scholar 

  9. Topunov, M.V., A Time-Optimal Nonlinear Problem, Avtom. Telemekh., 2002, no. 7, pp. 24–32.

    Google Scholar 

  10. Gantmakher, F.R., Teoriya matrits, Moscow: Nauka, 1988. Translated under the title The Theory of Matrices, New York: Chelsea, 1959.

    Google Scholar 

  11. Vakhrameev, S.A., Relay Theorems and Related Problems, Trudy Mat. Inst. Ross. Akad. Nauk, 1998, vol. 220, pp. 45–108.

    Google Scholar 

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  1. Moscow State Pedagogical University, Moscow, Russia

    M. V. Topunov

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  1. M. V. Topunov
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Topunov, M.V. Convexity of Reachable Sets of a Smooth Linear Control System in Phase Variables. Automation and Remote Control 65, 1761–1766 (2004). https://doi.org/10.1023/B:AURC.0000047890.03572.68

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  • DOI: https://doi.org/10.1023/B:AURC.0000047890.03572.68

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