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http://yadda.icm.edu.pl:80/baztech/element/bwmeta1.element.baztech-cd45fcf6-fac3-46c1-b186-4e72d7481c9e

Czasopismo

Control and Cybernetics

Tytuł artykułu

Extremals of the time optimal control problem for a material point moving along a straight line in the presence of friction and limitation on the velocity

Autorzy Osmolovskii, N. P.  Figura, A.  Kośka, M.  Wójtowicz, M. 
Treść / Zawartość http://control.ibspan.waw.pl
Warianty tytułu
Języki publikacji EN
Abstrakty
EN This paper provides an analysis of the time optimal control problem for a material point moving along a straight line in the presence of strength of resistance to movement (friction) and subject to constraint on the velocity. The point is controlled by a limited traction or braking force. The analysis of the problem is based on the maximum principle for state constraints in the Dubovitskii-Milyutin form, see Dubovitskii and Milyutin (1965), and the necessary second-order optimality condition for bang-bang controls, see Milyutin and Osmolovskii (1998).
Słowa kluczowe
EN material point   resistance forces   acceleration   deceleration   Pontryagin’s maximum principle   second order optimality conditions   optimal control   adjoint variable   state constraint   Stieltjes measure   singular arc   boundary arc  
Wydawca Systems Research Institute, Polish Academy of Sciences
Czasopismo Control and Cybernetics
Rocznik 2017
Tom Vol. 46, no. 4
Strony 305--324
Opis fizyczny Bibliogr. 17 poz., rys.
Twórcy
autor Osmolovskii, N. P.
  • University of Technology and Humanities, 26-600 Radom, ul. Malczewskiego 20A, Poland
  • Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447, Warszawa, Poland
  • Moscow State University of Civil Engineering, Jaroslavskoe shosse 26, Moscow, Russia
autor Figura, A.
  • University of Technology and Humanities, 26-600 Radom, ul. Malczewskiego 20A, Poland
autor Kośka, M.
  • University of Technology and Humanities, 26-600 Radom, ul. Malczewskiego 20A, Poland
autor Wójtowicz, M.
  • University of Technology and Humanities, 26-600 Radom, ul. Malczewskiego 20A, Poland
Bibliografia
[1] Asnis, I.A., Dmitruk, A.V., and Osmolovskii, N.P. (1985) Solution of the problem of the energetically optimal control of the motion of a train by the maximum principle. U.S.S.R. Comput. Maths. Math. Phys. 25 (6), 37-44.
[2] Cesari, L. (1983) Optimization – Theory and applications. Problems with ordinary differential equations. Applications of Mathematics 17, SpringerVerlag, New York.
[3] Dmitruk, A. V., Vdovina, A. K. (2016) Study of a One-Dimensional Optimal Control Problem with a Purely State-Dependent Cost. Differential Equations and Dynamical Systems 24 (3), 1-19.
[4] Dubovitskii, A.Ya., Milyutin, A.A. (1965) Extremum problems in the presence of restrictions. USSR Comput. Math. and Math. Phys. 5 (3), 1–80.
[5] Filippov, A.F. (1962) On certain questions in the theory of optimal control. SIAM J. Control 1, 76-84.
[6] Hartl, R.F., Sethi, S.P. and Vickson, R.G. (1995) A Survey of the Maximum Principles for Optimal Control Problems with State Constraints. SIAM Review 37 (2), 181-218.
[7] Lee, E.B., Markus, L. (1986) Foundations of Optimal Control Theory. Second edition, Robert E. Krieger Publishing Co., Inc., Melbourne, FL.
[8] Maurer, H. (1977) On optimal control problems with bounded state variables and control appearing linearly. SIAM J. Control and Optimization 15, 345-362.
[9] Maurer, H. (1979) On the minimum principle for optimal control problems with state constraints. Rechenzentrum der Universitat Munster, Report 41, Munster.
[10] Milyutin, A.A., Dmitruk, A.V., and Osmolovskii, N.P. (2004) Maximum principle in optimal control. Moscow State University, Faculty of Mechanics and Mathematics, Moscow (in Russian).
[11] Milyutin, A.A., Osmolovskii, N.P. (1998) Calculus of Variations and Optimal Control. American Mathematical Society, Providence, Rhode Island, 180.
[12] Osmolovskii, N., Figura, A., Koska, M. (2013) The fastest motion of a point on the plane. Technika Transportu Szynowego: koleje, tramwaje, metro 10, 49-56.
[13] Osmolovskii, N.P., Figura, A., Kośka, M., Wójtowicz, M. (2015) Extremals in the problem of minimum time obstacle avoidance for a 2D double integrator system. Control and Cybernetics, 44 (2), 185-209.
[14] Osmolovskii, N. P. and Maurer, H. (2012) Applications to Regular and Bang-Bang Control. Second-Order Necessary and Sufficient Optimality Conditions in Calculus of Variations and Optimal Control. SIAM, Philadelphia, PA.
[15] Osmolovskii, N., Wójtowicz, M., Janiszewski, S. (2013) Time optimal control for a two-dimensional linear system with a first order state constraint. Technika Transportu Szynowego: koleje, tramwaje, metro, nr 10/2013, 3039-3046.
[16] Pontryagin, L. S., Boltyanski, V. G., Gamkrelidze, R. V. and Mishchenko, E. F. (1964) The Mathematical Theory of Optimal Processes. Pergamon Press, New York.
[17] Young, L.C. (1969) Calculus of Variations and Optimal Control Theory. W. B. Saunders Company.
Uwagi
PL Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
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