A Compact Uncertainty Set
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.
KeywordsAdmissible Control Polar Cone Complementary Slackness Nontriviality Condition Stochastic Maximum Principle
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