Necessary Conditions for Impulsive Nonlinear Optimal Control Problems without a priori Normality Assumptions

  • A. Arutyunov
  • V. Dykhta
  • F. Lobo Pereira


First-order and second-order necessary conditions of optimality for an impulsive control problem that remain informative for abnormal control processes are presented and derived. One of the main features of these conditions is that no a priori normality assumptions are required. This feature follows from the fact that these conditions rely on an extremal principle which is proved for an abstract minimization problem with equality constraints, inequality constraints, and constraints given by an inclusion in a convex cone. Two simple examples illustrate the power of the main result.


Optimal impulsive control extremal principle second order optimality conditions abnormality 


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • A. Arutyunov
    • 1
  • V. Dykhta
    • 2
  • F. Lobo Pereira
    • 3
  1. 1.Department of Differential Equations and Functional AnalysisPeople Friendship University of RussiaMoscowRussia
  2. 2.Department of MathematicsBaikal State University of Economy and LawIrkutskRussia
  3. 3.Department of Electrotechnical and Computer Engineering, Faculty of EngineeringUniversity of PortoPortoPortugal

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