The commonly used definition of the index of DAE's (differential-algebraic equations) indicates how many times some algebraic equations have to be differentiated in order to transform a set of DAE's to a set of implicit ODE's. The differentiation can introduce higher-order derivatives of control variables and impulse responses of the system. In this paper we introduce a class of optimal control problems described by DAE's that can be optimized under the assumption that control variables are essentially bounded measurable functions. We show how to define adjoint equations for DAE's describing these problems. Finally, we propose algorithms which find controls satisfying optimality conditions in terms of the weak maximum principle.
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