A Survey on Optimal Control Problems with Differential-Algebraic Equations

The paper provides an overview on necessary and, whenever available, on sufficient conditions of optimality for optimal control problems with differential-algebraic equations (DAEs) and on numerical approximation techniques. Local and global minimum principles of Pontryagin type are discussed for convex linear-quadratic optimal control problems and for non-convex problems. The main steps for the derivation of such conditions will be explained. The basic working principles of different approaches towards the numerical solution of DAE optimal control problems are illustrated for direct shooting methods, full discretization techniques, projected gradient methods, and Lagrange–Newton methods in a function space setting.