Linear Multimodel Time Optimization

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


Robust time optimality can be considered as a particular case of the Lagrange problem, and therefore, the results obtained in the previous chapters allow us to formulate directly the Robust Maximum Principle for this time-optimization problem. As is shown in Chap.  8, the Robust Maximum Principle appears only as a necessary condition for robust optimality. But the specific character of the linear time-optimization problem permits us to obtain more profound results: in this case the Robust Maximum Principle appears as a necessary and sufficient condition. Moreover, for the linear robust time optimality it is possible to establish some additional results: the existence and uniqueness of robust controls, the piecewise constancy of robust controls for a polyhedral resource set, and a Feldbaum-type estimate for the number of intervals of constancy (or “switching”). All these aspects are studied below in detail.


Initial Point Convex Body Robust Control Admissible Control Transversality Condition 
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  1. Feldbaum, A. (1953), ‘Optimal processes in systems of automatic control’, Avtom. Telemeh. 14(6), 712–728 (in Russian). Google Scholar
  2. Poznyak, A.S. (2008), Advanced Mathematical Tools for Automatic Control Engineers, Vol. 1: Deterministic Technique, Elsevier, Amsterdam. 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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