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Second Order Optimality Conditions for Controls with Continuous and Bang-Bang Components

  • N. P. Osmolovskii
  • H. Maurer
Part of the IFIP International Federation for Information Processing book series (IFIPAICT, volume 202)

Abstract

Second order necessary and sufficient optimality conditions for bang-bang control problems in a very general form have been obtained by the first author. These conditions require the positive (semi)-definiteness of a certain quadratic form on the finite-dimensional critical cone. In the present paper we formulate a generalization of these results to optimal control problems where the control variable has two components: a continuous unconstrained control appearing nonlinearly and a bang-bang control appearing linearly and belonging to a convex polyhedron. Many examples of control of this kind may be found in the literature.

keywords

bang-bang control Pontryagin minimum principle second order necessary and sufficient conditions critical cone quadratic form strengthened Legendre condition 

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Copyright information

© International Federation for Information Processing 2006

Authors and Affiliations

  • N. P. Osmolovskii
    • 1
    • 2
  • H. Maurer
    • 3
  1. 1.Systems Research InstitutePolish Academy of SciencesWarszawaPoland
  2. 2.University of Podlasie in SiedlceSiedlcePoland
  3. 3.Institut für Numerische und Angewandte MathematikWilhelms-Universität MünsterMünsterGermany

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