— We consider the minimum time problem for a class of underwater vehicles. We focus on the situation of initial and final configurations at rest satisfying x0 = x f , z0 = z f , θ0 = θ f = 0. We supplement our theory with a numerical study of optimal bang–bang and singular solutions and include a discussion on a possible Fuller–like phenomenon.
Modeling strategies often result in dynamical systems of very high dimension. It is then desirable to find systems of the same form but of lower complexity, whose input-output behavior approximates the behavior of the original system. Here we consider linear time invariant (LTI) discrete time dy-namical systems. The cornerstone of this paper is a relation… (More)
The main focus of this paper is on an a-posteriori analysis for different model-order strategies applied to optimal control problems governed by linear parabolic partial differential equations. Based on a perturbation method it is deduced how far the suboptimal control, computed on the basis of the reduced-order model, is from the (unknown) exact one. For… (More)
This paper deals with H 2-norm optimal model reduction for linear time invariant continuous MIMO systems. We will give an overview on several representations of linear systems in state space as well as in Laplace space and discuss the H 2-norm for continuous MIMO systems with multiple poles. On this basis, necessary optimality conditions for the H 2-norm… (More)
In this paper the equivalences between necessary optimality conditions for H 2-norm optimal model reduction for linear time invariant continuous MIMO systems will be proven. Initially three main optimality conditions, namely the Interpolation conditions, Wilson conditions and Hyland-Bernstein conditions, were introduced. While the equivalence proof between… (More)
We present rigorous a posteriori output error bounds for reduced basis approximations of parametrized parabolic partial differential equations with non-affine source terms. The method employs the empirical interpolation method in order to construct affine coefficient-function approximations of the non-affine parametrized functions. Our a posteriori error… (More)
This dissertation is devoted to the development and study of new techniques in the field of model reduction for large-scale linear time-invariant (LTI) dynamical systems. The behavior of processes in electrical networks, mechanics, aeronautics, civil engineering , micro-electro-mechanical-systems, weather prediction and many others can be described by… (More)