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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 lead to highly nonlinear DAEs with low smoothness properties. They may have 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)

- Jingzhi Li, Jens Markus Melenk, Barbara Wohlmuth, Jun Zou, Samuel Ferraz-Leite, Christoph Ortner +11 others
- 2009

Higher order finite element methods are applied to 2D and 3D second order elliptic interface problems with smooth interfaces, and their convergence is analyzed in the H 1-and L 2-norm. The error estimates are expressed explicitly in terms of the approximation order p and a parameter δ that quantifies the mismatch between the smooth interface and the finite… (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)

Models for physical systems often take the form of implicit or behavioral models. One important problem is the identification of which combinations of variables are good candidtates for control variables. This paper first provides one solution to this problem for linear time varying systems. The solution is shown to be related to a general optimization… (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)