Extremals in the problem of minimum time obstacle avoidance for a 2D double integrator system

• Autorzy: Osmolovskii N. P. , Figura A. , Koska M. , Wojtowicz M.
• Języki publikacji: EN

Abstrakty

EN

This paper provides an analysis of time optimal control problem of motion of a material point in the plane outside the given circle, without friction. The point is controlled by a force whose absolute value is limited by one. The closure of exterior of the circle plays the role of the state constraint. The analysis of the problem is based on the minimum principle.

Słowa kluczowe

EN

necessary optimality condition; state constraint; optimal control; bang-bang control; Pontryagin principle

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2015
• Tom: Vol. 44, no. 2
• Strony: 185--209
• Opis fizyczny: Bibliogr. 7 poz., rys., tab.

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

Koska M.

• University of Technology and Humanities, 26-600 Radom, ul. Malczewskiego 20A, Poland

autor

Wojtowicz M.

• University of Technology and Humanities, 26-600 Radom, ul. Malczewskiego 20A, Poland

Bibliografia

• 1. Bonnans, J.F. and Hermant, A. (2009) Second-order analysis for optimal control problems with pure state constraints and mixed control-state constraints. Ann. Inst. Henri Poincare, Anal. Non Lineaire, 26, 561-598.
• 2. Dubovitskii, A. Ya. and Milyutin, A. A. (1965) Problems for extremum under constraints. Zh. Vychislit. Mat. i Mat. Fiz., 5, 3, 395-453; English transl. in U.S.S.R. Comput. Math. and Math. Phys. 5 (1965).
• 3. Girsanov, I.V. (1972) Lectures on Mathematical Theory of Extremum Problems (Translated from Russian). Lecture Notes in Economics and Mathematical Systems, 67, Springer-Verlag, Berlin Heidelberg-New York.
• 4. Ioffe, A.D. and Tikhomirov, V.M. (1974) Theory of Extremal Problems. Studies in Mathematics and Its Applications, 6, North-Holland Publishing Company, Amsterdam, 1979, Russian Edition: Nauka, Moscow, 1974.
• 5. Dubovitskii, A. Ya. and Milyutin, A. A. (1981) A Theory of the Maximum Principle. In: V.L. Levin, ed., Methods of the theory of extremal problems in economics. Nauka, Moscow, 6–47 (in Russian, see http:// www.milyutin.ru/).
• 6. Milyutin, A.A., Dmitruk, A.V., Osmolovskii, N.P. (2004) Maximum principle in optimal control. Moscow State University, Moscow (in Russian).
• 7. 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.