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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… (More)

We examine in this paper so-called B-critical points of linear, time-varying differential-algebraic equations (DAEs) of the form A(t)(D(t)x(t)) + B(t)x(t) = q(t). These critical or singular points, which cannot be handled by classical projector methods, require adapting a recently introduced framework based on Π-projectors. Via a continuation of certain… (More)

dedicated to C. W. Gear on the occasion of his 60th anniversary Abstract. In electric circuit simulation the charge oriented modiied nodal analysis may l e a d to highly nonlinear DAEs with low smoothness properties. They may h a ve index 2 but they do not belong to the class of Hessenberg form systems that are well understood. In the present paper, on the… (More)

We study the convergence behavior of collocation schemes applied to approximate solutions of BVPs in linear index 1 DAEs which exhibit a critical point at the left boundary. Such a critical point of the DAE causes a singularity within the inherent ODE system. We focus our attention on the case when the inherent ODE system is singular with a singularity of… (More)

When integrating regular ordinary differential equations numerically , one tries to match carefully the dynamics of the numerical algorithm with the dynamical behaviour of the true solution. The present paper deals with linear index-2 differential-algebraic systems. It is shown how knowledge pertaining to (numerical) regular ordinary differential equations… (More)

- D I S S E R T A T I O N, Herr Jan Dipl, Sieber, In Berlin, Mlynek, Krause Bodo +7 others

We investigate the longitudinal dynamics of semiconductor lasers using a model which couples a linear hyperbolic system of partial differential equations with ordinary differential equations. We prove the global existence and uniqueness of solutions using the theory of strongly continuous semigroups. Subsequently, we analyse the long-time behavior of the… (More)