PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2008 | Vol. 37, no 2 | 429-450
Tytuł artykułu

On singular arcs in nonsmooth optimal control

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we consider general optimal control problems (OCP) which are characterized by a nonsmooth ordinary state differential equation. However, we allow only mild types of nonsmoothness. More precisely, we assume that the right-hand side of the state equation is piecewise smooth and that the switching points, which separate these pieces, are determined as points, where a state-and possibly control-dependent (smooth) switching function changes sign. For this kind of optimal control problems necessary optimality conditions are developed. Attention is paid to the situation when the switching function vanishes identically along a nontrivial subarc. Such subarcs, which we call singular state subarcs, are investigated with respect to necessary conditions and to junction conditions. In extension to earlier results of the authors, Oberle and Rosendhal (2006), in this paper nonsmooth OCPs are considered with respect to the order of the switching function. Especially, the case of a zero-order switching function is included and examples of order zero, one and two are treated.
Wydawca

Rocznik
Strony
429-450
Opis fizyczny
Bibliogr. 16 poz., wykr.
Twórcy
  • Department of Mathematics, University of Hamburg, Hamburg, Germany
Bibliografia
  • ARROW, K.J. (1949) On the Use of Winds in Flight Planning. Journal of Meteorology 6, 150-159.
  • AUGUSTIN, D. and MAURER, H. (2000) Second Order Sufficient Conditions and Sensitivity Analysis for Optimal Multiprocess Control Problems. Control and Cybernetics 29, 11-31.
  • BAUMANN, H. (2002) Treibstoffminimale luftunterstützte Orbittransfers mit Flugbahnebenenwechsel. Doctoral Thesis, University of Hamburg.
  • BELL, D.J. and JACOBSON, D.H. (1975) Singular Optimal Control Problems. Academic Press, New York.
  • BRYSON, A.E. and Ho, Y.C. (1969) Applied Optimal Control. Ginn and Company, Waltham, Massachusetts.
  • CHUDEJ, K. (1995) Verallgemeinerte notwendige Bedingungen für zustandsbeschränkte Optimalsteuerungsaufgaben mit stückweise definierten Modellfunktionen. Zeitschrift für Angewandte Mathematik und Mechanik 75, 587-588.
  • CLARKE, F.H. (1983) Optimization and Nonsmooth Analysis. Wiley, New York.
  • CLARKE, F.H. and VINTER, R.B.(1989) Application of Optimal Multiprocesses. SIAM J. on Control and Optimization 27, 1048-1071, and 1071-1091.
  • HESTENES, M.R. (1966) Calculus of Variations and Optimal Control Theory. Wiley, New York.
  • MOVER, H.G. (2002) Deterministic Optimal Control. Trafford Publishing: Victoria, BC, Canada.
  • OBERLE, H.J. and ROSENDAHL, R. (2006) Numerical Computation of a Singular-State Subarc in an Economic Optimal Control Problem. Optimal Control Application and Methods 27, 211-235.
  • OBERLE, H.J. and GRIMM, W. (1989) BNDSCO - A Program for the numerical solution of optimal control problems. Report No. 515, Institut for Flight Systems Dynamics, Oberpfaffenhofen, German Aerospace Research Establishment DLR.
  • ROSENDAHL, R. (2008) Sufficient Optimally Conditions for Nonsmooth Optimal Control Problems. Doctoral Thesis, University of Hamburg.
  • STOER, J. and BULIRSCH, R. (1996) Introduction to Numerical Analysis. Texts in Applied Mathematics, Springer, New York.
  • ZERMELO, E. (1930) Über die Navigation in der Luft als Problem der Variationsrechnung. Annual report of the Deutsche-Mathematiker-Vereinigung 39, 44-48.
  • ZERMELO, E. (1931) Über das Navigationsproblem bei ruhender oder veränderlicher Windverteilung. ZAMM 11, 114-124.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0031-0076
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.