Optimal control of differential-algebraic equations without impulses

Optimal control problems involving differential-algebraic equations (DAEs) have been the focus of many research papers during the last years. First of all, theory for a linear-quadratic regulator was provided, then some generalizations were made for a general nonlinear problem. Soon it was discovered that optimal control theory for systems described by DAEs is complex because higher index systems have to be converted to index one systems and this usually requires differentiation of algebraic equations. As a result of this conversion control variables must be smooth enough to allow the differentiation otherwise systems response can have impulses not only in control variables but also in state trajectories. The assumption that control variables have higher order derivatives, or even that they are smooth, is too restrictive for real applications. In this paper we introduce a class of systems described by DAEs that can be optimized under reasonable assumptions