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Finite Collection of Dynamic Systems

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

Abstract

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.

Keywords

Robust Optimality Terminal Condition Admissible Control Uncertain System Maximality Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Boltyanski, V. (1975), ‘The tent method in the theory of extremal problems’, Usp. Mat. Nauk 30, 3–65 (in Russian). Google Scholar
  2. Boltyanski, V. (1987), ‘The tend method in topological vector spaces’, Sov. Math. Dokl. 34(1), 176–179. Google Scholar
  3. Dubovitski, A., & Milyutin, A. (1965), ‘Extremum problems with constrains’, Zh. Vychisl. Mat. Mat. Fiz. 5(3), 395–453. Google Scholar

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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