Local Minimum Principle for Optimal Control Problems Subject to Index One Differential-algebraic Equations

Necessary conditions in terms of a local minimum principle are derived for optimal control problems subject to index-1 differential-algebraic equations, pure state constraints and mixed control-state constraints. Differential-algebraic equations are composite systems of differential equations and algebraic equations, which frequently arise in practical applications. The local minimum principle is based on necessary optimality conditions for general infinite optimization problems. The special structure of the optimal control problem under consideration is exploited and allows to obtain more regular representations for the multipliers involved. An additional Mangasarian-Fromowitz like constraint qualification for the optimal control problem ensures the regularity of a local minimum.