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Optimal control of differential-algebraic equations of higher index. I: First-order approximations. (English) Zbl 1129.49032

Summary: This paper deals with optimal control problems described by higher index DAEs. We introduce a class of these problems which can be transformed to index one control problems. For this class of higher index DAEs, we derive first-order approximations and adjoint equations for the functionals defining the problem. These adjoint equations are then used to state, in the accompanying paper, the necessary optimality conditions in the form of a weak maximum principle. The constructive way used to prove these optimality conditions leads to globally convergent algorithms for control problems with state constraints and defined by higher index DAEs.

MSC:

49K15 Optimality conditions for problems involving ordinary differential equations
34M15 Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain

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