linear-quadratic optimal control problems feedback control differential-algebraic equations descriptor systems Riccati equations Hamiltonian systems Feedback solutions of optimal control problems with DAE constraints Galina A. Kurina Kurina Galina A. Roswitha März März Roswitha Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976),

Feedback solutions of optimal control problems with DAE constraints

Galina A. Kurina , Roswitha März

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976),

MSC 2000

49N10 Linear-quadratic problems
49J15 Optimal control problems involving ordinary differential equations

Abstract
An optimal feedback control has been obtained for linear-quadratic optimal control problems with constraints described by differential-algebraic equations. 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 those strong consistency conditions as used in several previous papers.\\ Also the solvability of the resulting closed loop system is considered and the relations between Riccati equations and Hamiltonian systems are elucidated.

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