Finite Collection of Dynamic Systems

  • Vladimir G. Boltyanski
  • Alexander S. Poznyak
Part of the Systems & Control: Foundations & Applications book series (SCFA)


The general approach to the Min-Max Control Problem for uncertain systems, based on the suggested version of the Robust Maximum Principle, is presented. The uncertainty set is assumed to be finite, which leads to a direct numerical procedure realizing the suggested approach. It is shown that the Hamilton function used in this Robust Maximum Principle is equal to the sum of the standard Hamiltonians corresponding to a fixed value of the uncertainty parameter. The families of differential equations of the state and conjugate variables together with transversality and complementary slackness conditions are demonstrated to form a closed system of equations, sufficient to construct a corresponding robust optimal control.


Robust Optimality Terminal Condition Admissible Control Uncertain System Maximality Condition 
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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Vladimir G. Boltyanski
    • 1
  • Alexander S. Poznyak
    • 2
  1. 1.CIMATGuanajuatoMexico
  2. 2.Automatic Control DepartmentCINVESTAV-IPNMéxicoMexico

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