Title:

Equivalence of second order optimality conditions for bang–bang control problems. Part 2 : Proofs, variational derivatives and representations

Subtitle:

Raport Badawczy = Research Report ; RB/85/2007

Creator:

Osmolovskii, Nikolai ; Maurer, Helmut

Publisher:

Instytut Badań Systemowych. Polska Akademia Nauk ; Systems Research Institute. Polish Academy of Sciences

Place of publishing:

Warszawa

Date issued/created:

2007

Description:

5-45 stron ; 21 cm ; Bibliografia s. 45

Abstract:

In Part 1 of this paper (Osmolovskii and Maurer, 2005), we have summarized the main results on the equivalence of two quadratic forms from which second order necessary and sufficient conditions can be derived for optimal bang-bang control problems. Here, in Part 2, we give detailed proofs and elaborate explicit rela- tions between Lagrange multipliers and elements of the critical cones in both approaches. The main analysis concerns the derivation of formulas for the first and second order derivatives of trajectories with respect to variations of switching times, initial and final time and ini- tial point. This leads to explicit representations of the second order derivatives of the Lagrangian for the induced optimization problem. Based on a suitable transformation, we obtain the elements of the Hessian of the Lagrangian in a form which involves only first order variations of the nominal trajectory. Finally, a careful regrouping of all terms allows us to find the desired equivalence of the two quadratic forms.

Relation:

Raport Badawczy = Research Report

Resource type:

Tekst

Detailed Resource Type:

Raport

Source:

RB-2007-85

Language:

eng

Language of abstract:

eng

Rights:

Licencja Creative Commons Uznanie autorstwa 4.0

Terms of use:

Zasób chroniony prawem autorskim. [CC BY 4.0 Międzynarodowe] Korzystanie dozwolone zgodnie z licencją Creative Commons Uznanie autorstwa 4.0, której pełne postanowienia dostępne są pod adresem: ; -

Digitizing institution:

Instytut Badań Systemowych Polskiej Akademii Nauk

Original in:

Biblioteka Instytutu Badań Systemowych PAN

Projects co-financed by:

Program Operacyjny Polska Cyfrowa, lata 2014-2020, Działanie 2.3 : Cyfrowa dostępność i użyteczność sektora publicznego; środki z Europejskiego Funduszu Rozwoju Regionalnego oraz współfinansowania krajowego z budżetu państwa

Access:

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