A Compact Uncertainty Set

Part of the Systems & Control: Foundations & Applications book series (SCFA)


This chapter extends the possibilities of the MP approach for a class of Min-Max control problems for uncertain models given by a system of stochastic differential equations with a controlled diffusion term and unknown parameters within a given measurable compact set. For simplicity, we consider the Min-Max problem belonging to the class of optimization problems with a fixed finite horizon where the cost function contains only a terminal term (without an integral part). The proof is based on the Tent Method in a Banach space, discussed in detail in Part II; it permits us to formulate the necessary conditions of optimality in the Hamiltonian form.


Admissible Control Polar Cone Complementary Slackness Nontriviality Condition Stochastic Maximum Principle 
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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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