A maximum principle for optimal control problems with mixed constraints
Maria do Rosário de Pinho · IMA Journal of Mathematical Control and Information · 2001
Necessary conditions in the form of maximum principles are derived for optimal control problems with mixed control and state constraints. Traditionally, necessary condtions for problems with mixed constraints have been proved under hypothesis which include the requirement that the Jacobian of the mixed constraint functional, with respect to the control variable, have full rank. We show that it can be replaced by a weaker ‘interiority’ hypothesis. This refinement broadens the scope of the optimality conditions, to cover some optimal control problems involving differential algebraic constraints, with index greater than unity.