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An optimal feedback control has been obtained for linear-quadratic optimal control problems with constraints described by differential-algebraic equations (DAEs). For that purpose, a new implicit Riccati equation (Riccati differential-algebraic system) is provided, and its solvability is investigated. It is shown that one can do without the strong consistency conditions as used in several previous papers. Furthermore, the solvability of the resulting closed loop system is considered and the relations between Riccati equations and Hamiltonian systems are elucidated.

Feedback Solutions of Optimal Control Problems with DAE Constraints