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.
• 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).