Second order optimality conditions for bang-bang control problems

• Autorzy: Maurer H. , Osmolovskii N. P.
• Języki publikacji: EN

Abstrakty

EN

Second order necessary and sufficient optimality conditions for bang-bang control problems have been studied in Milyutin, Osmolovskii (1998). These conditions amount to testing the positive (semi-)definiteness of a quadratic form on a critical cone. The assumptions are appropriate for numerical verification only in some special cases. In this paper, we study various transformations of the quadratic form and the critical cone which will be tailored to different types of control problems in practice. In particular, by means of a solution to a linear matrix differential equation, the quadratic form can be converted to perfect squares. We demonstrate by three practical examples that the conditions obtained can be verified numerically.

Słowa kluczowe

EN

bang-bang control; second order necessary and sufficient conditions; critical cone; transformation of quadratic forms; numerical verification of second order conditions; van der Pol oscillator

PL

sterowanie przekaźnikowe

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2003
• Tom: Vol. 32, no 3
• Strony: 555--584
• Opis fizyczny: Bibliogr. 43 poz., wykr.

Twórcy

autor

Maurer H.

• Westfalische Wilhelms–Universitat Munster Institut fur Numerische Mathematik Einsteinstr. 62, D–48149 Munster, Germany

autor

Osmolovskii N. P.

• Department of Applied Mathematics Moscow State Civil Engineering University (MISI) Yaroslavskoe sh., 26, 129337 Moscow, Russia

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