Necessary Conditions for Optimal Control Problems Involving Nonlinear Differential Algebraic Equations

Dynamic models which take the form of a coupled set of differential and algebraic equations DAEs. are widely used in process systems engineering. Necessary conditions of optimality for optimal control problems involving such models are derived. A strong Maximum Principle is obtained under a convexity hypothesis on the velocity set. An example illustrates that the strong Maximal Principle may be violated when this hypothesis is dropped. For problems involving nonconvex velocity sets, however, a weak Maximum Principle is valid.