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In this work, the existence, uniqueness and regularity of solutions to the time-dependent Kohn-Sham equations are investigated. The Kohn-Sham equations are a system of nonlinear coupled Schrödinger equations that describe multi-particle quantum systems in the framework of the time dependent density functional theory. In view of applications with control problems, the presence of a control function and of an inhomogeneity are also taken into account. * Supported in part by the Deutsche Forschungsgemeinschaft (DFG) project "Controllability and Optimal Control of Interacting Quantum Dynamical Systems" (COCIQS).

Many application models in quantum physics and chemistry require to control multielectron systems to achieve a desired target configuration. This challenging task appears possible in the framework of time-dependent density functional theory (TDDFT) that allows to describe these systems while avoiding the high dimensionality resulting from the multi-particle Schrödinger equation. For this purpose, the theory and numerical solution of optimal control problems governed by a Kohn-Sham TDDFT model are investigated, considering different objectives and a bilinear control mechanism. Existence of optimal control solutions and their characterization as solutions to Kohn-Sham TDDFT optimality systems are discussed. To validate this control framework, a time-splitting discretization of the optimality systems and a nonlinear conjugate gradient scheme are implemented. Results of numerical experiments demonstrate the computational capability of the proposed control approach.

Abstract. This paper describes the mechanical and electrical design, as well as the control strategy, of the FU-Fighters robots, a F180 league team that won the second place at RoboCup'99. It explains how we solved the computer vision and radio communication problems that arose in the course of the project. The paper mainly discusses the hierarchical control architecture used to generate the behavior of individual agents and the team. Our reactive approach is based on the Dual Dynamics framework developed by H. Jäger, in which activation dynamics determines when a behavior is allowed to influence the actuators, and a target dynamics establishes how this is done. We extended the original framework by adding a third module, the perceptual dynamics. Here, the readings of fast changing sensors are aggregated temporarily to form complex, slow changing percepts. We describe the bottom-up design of behaviors and illustrate our approach using examples from the RoboCup domain.

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