Optimal control with DAE constraints

In this paper we discuss a kind of optimal control problems with restricted control variables, and the state equations of which are depicted by differential-algebraic equations(DAEs). Through analyzing characters of the optimal control model with DAE constraints, the model can be transformed into a functional extreme value problem. Then by means of the variational principle, we present necessary conditions of optimality for the functional extreme value problems. In addition, a minimum condition of optimality is given based on the necessary conditions. Those theoretical results also provide an analytical way for solving optimal control problems(OCPs). Finally, a well-known chemical engineering model is shown to explain our results.