Minimax optimal control problem with state constraints

In this article, nondegenerate necessary conditions of optimality are derived and discussed for the so-called “minimax” optimal control problems with state constraints. In this class of problems, the data depends on an unknown parameter that takes values in a given compact set called “uncertainty set”. The solution of the problem is considered for the worst case value of the unknown parameter. The result is obtained in the two stages: after the basic necessary conditions of optimality are derived, additional conditions ensuring their nondegeneracy in the minimax context are obtained.